The eighth term of an AP is half its second term and the eleventh term exceeds one third of its fourth term by 1. Find the 15th term. - Mathematics

Advertisements
Advertisements
Sum

The eighth term of an AP is half its second term and the eleventh term exceeds one third of its fourth term by 1. Find the 15th term.

Advertisements

Solution

Let a and d the first term and common difference of an AP, respectively.

Now, by given condition,

a8 = `1/2 a_2`

⇒ a + 7d = `1/2 (a + d)`  ...[∵ an = a + (n – 1)d]

⇒ 2a + 14d = a + d

⇒ a + 13d = 0  ...(i)

And a11 = `1/3 a_4 + 1` ...[Given]

⇒ a + 10d = `1/3[a + 3d] + 1`

⇒ 3a + 30d = a + 3d + 3

⇒ 2a + 27d = 3

From equations (i) and (ii),

2(–13d) + 27d = 3

⇒ –26d + 27d = 3

⇒ d = 3

From equation (i),

a + 13(3) = 0

⇒ a = – 39

∴ a15 = a + 14d

= – 39 + 14(3)

= – 39 + 42

= 3

  Is there an error in this question or solution?
Chapter 5: Arithematic Progressions - Exercise 5.4 [Page 57]

APPEARS IN

NCERT Exemplar Mathematics Class 10
Chapter 5 Arithematic Progressions
Exercise 5.4 | Q 3 | Page 57

RELATED QUESTIONS

Write the first two terms of the sequence whose nth term is tn = 3n ‒ 4.


State whether the following sequence is an A.P. or not?

1, 4, 7, 10, ………………..


For an A.P. t3 = 8 and t4 =12, find the common difference d.


The 10th term of an A.P. is 52 and 16th term is 82. Find the 32nd term and the general term


Write first four terms of the A.P. when the first term a and the common differenced are given as follows:

 a = 10, d = 10


Write the next two terms of A.P. whose first term is 3 and the common difference is 4.


Find next two terms of an A.P. 

4, 9, 14, ......


If `S_5 = 15` and `S_6 = 21`, Find `t_6`.


Find n if the nth term of the following A.P. is 68

5, 8, 11, 14, ..........


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 15th row and also find how many total seats are there in the auditorium ?


Find the common difference of the A.P. and write the next two terms 75, 67, 59, 51, ...


Write the 25th term of an A.P. 12,16,20,24, ....... 


First term a and common difference d are given below. Find the corresponding A.P.

a = `3/4`, d = `1/2`


Find the first term and common difference of the Arithmetic Progressions whose nth term is given below

tn = – 3 + 2n


Which term of an A.P. 16, 11, 6, 1, ... is – 54?


Find the middle term(s) of an A.P. 9, 15, 21, 27, …, 183.


In a theatre, there are 20 seats in the front row and 30 rows were allotted. Each successive row contains two additional seats than its front row. How many seats are there in the last row?


The sum of three consecutive terms that are in A.P. is 27 and their product is 288. Find the three terms


The first term of an arithmetic progression is unity and the common difference is 4. Which of the following will be a term of this A.P.


If 6 times of 6th term of an A.P. is equal to 7 times the 7th term, then the 13th term of the A.P. is


If (m + 1)th term of an A.P. is twice the (n + 1)th term, then prove that (3m + 1)th term is twice the (m + n + 1)th term


Two A.P.’s have the same common difference. The first term of one A.P. is 2 and that of the other is 7. Show that the difference between their 10th terms is the same as the difference between their 21st terms, which is the same as the difference between any two corresponding terms.


Choose the correct alternative answer for the following sub question

For an A.P. 5, 12, 19, 26, … a = ?


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


Choose the correct alternative answer for the following sub question

In an A.P., 0, – 4, – 8, – 12, ... find t2 = ?


Find d if t9 = 23 व a = 7


Merry got a job with salary ₹ 15000 per month. If her salary increases by ₹ 100 per month, how much would be her salary after 20 months?


For an A.P., t4 = 12 and its common difference d = – 10, then find tn 


Find 27th and nth term of given A.P. 5, 2, – 1, – 4, ......


Which of the following form an AP? Justify your answer.
0, 2, 0, 2,...


Justify whether it is true to say that `-1, - 3/2, -2, 5/2,...` forms an AP as a2 – a1 = a3 – a2.


Verify that the following is an AP, and then write its next three terms.

`0, 1/4, 1/2, 3/4, ...`


Split 207 into three parts such that these are in AP and the product of the two smaller parts is 4623.


Write second and third term of an A.P. whose first term is 6 and common difference is – 3.


First term and common difference of an A.P. are 1 and 2 respectively; find S10.

Given: a = 1, d = 2

find S10 = ?

Sn = `n/2 [2a + (n - 1) square]`

S10 = `10/2 [2 xx 1 + (10 - 1)square]`

= `10/2[2 + 9 xx square]`

= `10/2 [2 + square]`

= `10/2 xx square = square`


If six times of the 3rd term is equal to the eight times of 7th term in an A.P., then what will be the 19th term?


How many terms are present in the sequence of A.P. 6, 11, 16, 21, ......... whose sum is 969?


The sum of the squares of five consecutive natural numbers is 1455. Find the numbers.


If k + 2, 4k – 6 and 3k – 2 are three consecutive terms of an A.P., then the value of k is ______.


Statement A (Assertion): `-5, (-5)/2, 0, 5/2`, .... is in Arithmetic Progression.

Statement R (Reason): The terms of an Arithmetic Progression cannot have both positive and negative rational numbers.


Share
Notifications



      Forgot password?
Use app×