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Chapter 5 · Question 6

Find the sum of the first 15 terms of the AP $5,8,11,\ldots$ .

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Q6

Find the sum of the first 15 terms of the AP $5,8,11,\ldots$ .

Answer Revealed

Direct Answer:

Here

a=5

,

d=3

,

n=15

.

S_{15}=\frac{15}{2}[2(5)+14(3)]=\frac{15}{2}(52)=390

.

Simple Explanation

Use the AP sum formula. The sum is

390

.

Exam-Ready Structure

For

5,8,11,\ldots

,

a=5

and

d=3

. Then

S_n=\frac n2[2a+(n-1)d]

. Thus

S_{15}=\frac{15}{2}[10+14\times3]=\frac{15}{2}(52)=390

.

Key Points

Here $a=5$ , $d=3$ , $n=15$ .
Use the NCERT formula or theorem carefully.
Write units and final conclusion where applicable.

Related Questions

What is an arithmetic progression? Find the common difference of $45,43,41,39,\ldots$ .

State the formula for the $n$ th term of an AP and use it to find the 20th term of $3,7,11,15,\ldots$ .

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