###### Advertisements

###### Advertisements

If the nth term of an AP is (2n + 1) then find the sum of its first three terms

If the *n*^{th} term of an A.P. is (2*n* + 1), then the sum of its first three terms is

#### Options

A. 6

*n*+ 3B. 15

C. 12

D. 21

###### Advertisements

#### Solution 1

∵ a_{n} = 2n + 1

a_{1} = 2(1) + 1 = 3

a_{2} = 2(2) + 1 = 5

a_{3} = 2(3) + 1 = 7

∴ a_{1} + a_{2} + a_{3} = 3 + 5 + 7 = 15

#### Solution 2

**Given:** The *n*^{th} term of A.P. i.e., *a*_{n} = 2*n* + 1

**To find:** Sum of first three terms

On putting *n* = 1, 2 and 3, we obtain:

*a*_{1} = 2 × 1 + 1 = 2 + 1 = 3

*a*_{2} = 2 × 2 + 1 = 4 + 1 = 5

*a*_{3} = 2 × 3 + 1 = 6 + 1 = 7

∴ Sum of first three terms *a*_{1} + *a*_{2} + *a*_{3} = 3 + 5 + 7 = 15

Hence, the correct answer is B.

#### APPEARS IN

#### RELATED QUESTIONS

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

1, 4, 7, 10, ………………..

State whether the following sequence is an AP or not: 1, 3, 6, 10………

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

**In which of the following situations, does the list of number involved make as arithmetic progression and why?**

The cost of digging a well after every metre of digging, when it costs Rs 150 for the first metre and rises by Rs 50 for each subsequent metre.

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

a = - 1.25, d = - 0.25

Which of the following are APs? If they form an A.P. find the common difference *d* and write three more terms:

`-1/2, -1/2, -1/2, -1/2` ....

Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.

12, 2, −8, −18, ...

Find n if the given value of x is the nth term of the given A.P.

`1, 21/11, 31/11, 41/11,......, x = 171/11`

For what value of *k* will the consecutive terms 2*k* + 1, 3*k* + 3 and 5*k* − 1 form an AP?

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 ?

The first term and the common difference of an A. P. is 10,000 and

2000 resectively. Find the sum of first 12 terms of the A.P.

How many three digit numbers are divisible by 7?

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

The product of four consecutive positive integers is 840. Find the numbers.

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

a = 7, d = – 5

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 n^{th} term is given below

t_{n} = – 3 + 2n

Find the 19^{th} term of an A.P. – 11, – 15, – 19, ...

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.

If 3 + k, 18 – k, 5k + 1 are in A.P. then find k

Find x, y and z, given that the numbers x, 10, y, 24, z are in A.P.

Priya earned ₹ 15,000 in the first month. Thereafter her salary increased by ₹ 1500 per year. Her expenses are ₹ 13,000 during the first year and the expenses increase by ₹ 900 per year. How long will it take for her to save ₹ 20,000 per month

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.

**Choose the correct alternative answer for the following sub question**

For an A.P. 5, 12, 19, 26, … a = ?

**Choose the correct alternative answer for the following sub-question**

Find t_{3} = ? in an A.P. 9, 15, 21, 27, ...

Common difference, d = ? for the given A.P., 7, 14, 21, 28 ........

Activity :- Here t_{1} = 7, t_{2} = 14, t_{3} = 21, t_{4} = `square`

t_{2} − t_{1} = `square`

t_{3} – t_{2} = 7

t_{4} – t_{3} = `square`

Therefore, common difference d = `square`

Find first four terms of an A.P., whose first term is 3 and common difference is 4.

In an A.P. a = 4 and d = 0, then find first five terms

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?

If a, b, c, d, e are in A.P., then the value of a - 4b + 6c - 4d + e is ______.

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

For an A.P., if a = 7 and d = 2.5 then t_{12} = ?

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

If the terms 10, a, 40 are in A.P., then find the value of a.

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

The school auditorium was to be constructed to accommodate at least 1500 people. The chairs are to be placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one.

- If the first circular row has 30 seats, how many seats will be there in the 10
^{th}row? - For 1500 seats in the auditorium, how many rows need to be there?

OR

If 1500 seats are to be arranged in the auditorium, how many seats are still left to be put after the 10^{th}row? - If there were 17 rows in the auditorium, how many seats will be there in the middle row?

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

Treasure Hunt is an exciting and adventurous game where participants follow a series of clues/numbers/maps to discover hidden treasure. Players engage in a thrilling quest, solving puzzles and riddles to unveil the location of the coveted prize. While playing a treasure hunt game, some clues (numbers) are hidden in various spots collectively forming an A.P. If the number on the nth spot is 20 + 4n, then answer the following questions to help the players in spotting the clues: |

- Which number is on first spot? 1

- Which spot is numbered as 112? 2

OR - What is the sum of all the numbers on the first 10 spots? 2

- Which spot is numbered as 112? 2
- Which number is on the (n – 2)
^{th}spot? 1