#### Chapters

## Chapter 3 - Arithmetic Progression

#### Pages 6 - 62

Which of the following sequences are A.P. ? If they are A.P. find the common difference .

2, 4, 6, 8,....

Which of the following sequences are A.P. ? If they are A.P. find the common difference .

Which of the following sequences are A.P. ? If they are A.P. find the common difference .

–10, –6, –2, 2...

Which of the following sequences are A.P. ? If they are A.P. find the common difference .

0.3, 0.33, 0.333,...

Which of the following sequences are A.P. ? If they are A.P. find the common difference .

0, –4, –8, –12,...

Which of the following sequences are A.P. ? If they are A.P. find the common difference .

Which of the following sequences are A.P. ? If they are A.P. find the common difference .

Which of the following sequences are A.P. ? If they are A.P. find the common difference .

127, 132, 137,...

Write an A.P. whose first term is a and common difference is *d* in each of the following.

*a* = 10, *d* = 5

Write an A.P. whose first term is a and common difference is *d* in each of the following.

*a* = –3, *d* = 0

Write an A.P. whose first term is a and common difference is *d* in each of the following.

*a*= –7,

*d*= \[\frac{1}{2}\]

Write an A.P. whose first term is a and common difference is *d* in each of the following.

*a* = –1.25, *d* = 3

Write an A.P. whose first term is a and common difference is *d* in each of the following.

*a* = 6, *d* = –3

Write an A.P. whose first term is a and common difference is *d* in each of the following.

*a* = 19, *d* = –4

Find the first term and common difference for each of the A.P.

5, 1, –3, –7,...

Find the first term and common difference for each of the A.P.

0.6, 0.9, 1.2,1.5,...

Find the first term and common difference for each of the A.P.

127, 135, 143, 151,...

Find the first term and common difference for each of the A.P.

#### Pages 62 - 66

Write the correct number in the given boxes from the following A. P.

1, 8, 15, 22,...

Here *a* =Here *a* = *t*_{1 }= , *t*_{2} = , *t*_{3} = ,

t_{2} –* t*_{1} = – = *t*_{3} – *t*_{2} = – = ∴ *d* =

Write the correct number in the given boxes from the following A. P.

3, 6, 9, 12,...

Here *t*_{1 }= *t*_{2} = , *t*_{3} = , *t*_{4} = ,*t*_{2} –* t*_{1} = , *t*_{3} – *t*_{2} = ∴ *d* =

Write the correct number in the given boxes from the following A. P.

–3, –8, –13, –18,...

Here *t*_{3 }= , *t*_{2} = , *t*_{4} =, *t*_{1} = ,*t*_{2} –* t*_{1} = , *t*_{3} – *t*_{2} = ∴ *a* = , *d* =

Write the correct number in the given boxes from the following A. P.

70, 60, 50, 40,...

Here *t*_{1 }= , *t*_{2} = , *t*_{3} = ,...

∴ *a* = , *d* =

Decide whether following sequence is an A.P., if so find the 20^{th} term of the progression.

–12, –5, 2, 9, 16, 23, 30,...

Given Arithmetic Progression 12, 16, 20, 24, . . . Find the 24^{th} term of this progression.

Find the 19^{th} term of the following A.P.

7, 13, 19, 25,....

Find the 27^{th} term of the following A.P.

9, 4, –1, –6, –11,...

Find how many three digit natural numbers are divisible by 5.

The 11^{th} term and the 21^{st} term of an A.P. are 16 and 29 respectively, then find the 41^{th}term of that A.P.

In the natural numbers from 10 to 250, how many are divisible by 4?

In an A.P. 17^{th} term is 7 more than its 10^{th} term. Find the common difference.

#### Pages 72 - 73

_{27}.

Find the Sum of First 123 Even Natural Numbers.

In an A.P. 19^{th} term is 52 and 38^{th }term is 128, find sum of first 56 terms.

Complete the following activity to find the sum of natural numbers from 1 to 140 which are divisible by 4.

Sum of numbers from 1 to 140, which are divisible by 4 =

Sum of first 55 terms in an A.P. is 3300, find its 28^{th} term.

In an A.P. sum of three consecutive terms is 27 and their product is 504, find the terms.

( Assume that three consecutive terms in A.P. are *a* – *d* , *a* , *a* +* d* ).

Find four consecutive terms in an A.P. whose sum is 12 and sum of 3^{rd} and 4^{th} term is 14.(Assume the four consecutive terms in A.P. are *a* – *d*, *a*, *a* + *d*, *a* +2*d*)

If the 9^{th} term of an A.P. is zero then show that the 29^{th }term is twice the 19^{th} term ?

#### Page 78

On 1st Jan 2016, Sanika decides to save Rs 10, Rs 11 on second day, Rs 12 on third day. If she decides to save like this, then on 31^{st} Dec 2016 what would be her total saving ?

A man borrows Rs 8000 and agrees to repay with a total interest of Rs 1360 in 12 monthly instalments. Each instalment being less than the preceding one by Rs 40. Find the amount of the first and last instalment.

Sachin invested in a national saving certificate scheme. In the first year he invested Rs 5000 , in the second year Rs 7000, in the third year Rs 9000 and so on. Find the total amount that he invested in 12 years.

There is an auditorium with 27 rows of seats. There are 20 seats in the first row, 22 seats in the second row, 24 seats in the third row and so on. Find the number of seats in the 15^{th} row and also find how many total seats are there in the auditorium ?

Kargil’s temperature was recorded in a week from Monday to Saturday. All readings were in A.P. The sum of temperatures of Monday and Saturday was 5°C more than sum of temperatures of Tuesday and Saturday. If temperature of Wednesday was –30° celsius then find the temperature on the other five days.

On the world environment day tree plantation programme was arranged on a land which is triangular in shape. Trees are planted such that in the first row there is one tree, in the second row there are two trees, in the third row three trees and so on. Find the total number of trees in the 25 rows.

#### Pages 78 - 80

Choose the correct alternative answer for the following question .

The sequence –10, –6, –2, 2,...

Choose the correct alternative answer for the following question .

First four terms of an A.P. are ....., whose first term is –2 and common difference is –2.

(A) -2,0,2,4 (B) -2,4 ,-8,16

(C)-2, -4,-6,-8 (D) -2, -4 ,-8,-16

Choose the correct alternative answer for the following question .

What is the sum of the first 30 natural numbers ?

Choose the correct alternative answer for the following question .

For an given A.P. *t*_{7} = 4,* d* = –4, *n* = 101, then *a* = ....

(A) 6 (B) 7 (C) 20 (D) 28

Choose the correct alternative answer for the following question .

For an given A.P. *a* = 3.5,* d* = 0, *n* = 101, then* *t* _{n}* = ....

(A) 0 (B) 3.5 (C) 103.5 (D)14.5

Choose the correct alternative answer for the following question .

In an A.P. first two terms are –3, 4 then 21^{st} term is ...

(A) -143 (B) 143 (C) 137 (D) 17

Choose the correct alternative answer for the following question .

If for any A.P. *d* = 5 then t_{18} – t_{13} = ....

(A) 5 (B) 20 (C) 25 (D) 30

Choose the correct alternative answer for the following question .

Sum of first five multuiples of 3 is...

(A) 45 (B) 55 (C) 15 (D) 75

Choose the correct alternative answer for the following question .

15, 10, 5,... In this A.P sum of first 10 terms is...

(A) -75 (B) -125 (C) 75 (D) 125

Choose the correct alternative answer for the following question .

In an A.P. 1^{st} term is 1 and the last term is 20. The sum of all terms is = 399 then *n* = ....

(A) 42 (B) 38 (C) 21 (D) 19

Find the fourth term from the end in an A.P. –11, –8, –5,...., 49.

In an A.P. the 10^{th} term is 46 sum of the 5^{th} and 7^{th} term is 52. Find the A.P.

The A.P. in which 4^{th} term is –15 and 9^{th} term is –30. Find the sum of the first 10 numbers.

Two A.P.’ s are given 9, 7, 5, . . . and 24, 21, 18, . . . . If *n*^{th} term of both the progressions are equal then find the value of *n* and *n* th term.

If sum of 3^{rd} and 8^{th} terms of an A.P. is 7 and sum of 7^{th} and 14^{th} terms is –3 then find the 10 th term .

In an A.P. the first term is –5 and last term is 45. If sum of all numbers in the A.P. is 120, then how many terms are there ? What is the common difference ?

Sum of 1 to *n* natural numbers is 36, then find the value of *n* .

Divide 207 in three parts, such that all parts are in A.P. and product of two smaller parts will be 4623.

There are 37 terms in an A.P., the sum of three terms placed exactly at the middle is 225 and the sum of last three terms is 429. Write the A.P.

If first term of an A.P. is *a*, second term is *b* and last term is *c*, then show that sum of all terms is \[\frac{\left( a + c \right) \left( b + c - 2a \right)}{2\left( b - a \right)}\].

If the sum of first p terms of an A.P. is equal to the sum of first q terms then show that the sum of its first (p + q) terms is zero. (p ≠ q)?

If m times the m^{th} term of an A.P. is eqaul to n times n^{th} term then show that the (m + n)^{th }term of the A.P. is zero.

Rs 1000 is invested at 10 percent simple interest. Check at the end of every year if the total interest amount is in A.P. If this is an A.P. then find interest amount after 20 years. For this complete the following activity.

#### Textbook solutions for Class 10th Board Exam

## Balbharati solutions for Class 10th Board Exam Algebra chapter 3 - Arithmetic Progression

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Concepts covered in Class 10th Board Exam Algebra chapter 3 Arithmetic Progression are Terms in a sequence, Geometric Mean, Arithmetic Mean, Sum of the First 'N' Terms of an Geometric Progression, Sum of First n Terms of an AP, General Term of an Geomatric Progression, General Term of an Arithmetic Progression, Geometric Progression, Arithmetic Progression, Introduction to Sequence, Arithmetic Progression Examples and Solutions.

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