MCQ

Sum

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

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#### 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.

Concept: Arithmetic Progression

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