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Chapter 5 · Question 4

State the formula for the sum of first $n$ terms of an AP. Find the sum of first 20 natural numbers.

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Answer

Direct Answer

The sum is

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

or

S_n=\frac n2(a+l)

. For natural numbers,

a=1

,

d=1

,

n=20

, so

S_{20}=\frac{20}{2}(1+20)=210

.

Simple Explanation

Use

S_n=n(a+l)/2

. The first 20 natural numbers add to

210

.

Exam-Ready Structure

For an AP,

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

. If the last term

l

is known,

S_n=\frac n2(a+l)

. For

1,2,3,\ldots,20

,

a=1

,

l=20

,

n=20

. Therefore

S_{20}=\frac{20}{2}(1+20)=10\times21=210

.

Key Points

The sum is $S_n=\frac n2[2a+(n-1)d]$ or $S_n=\frac n2(a+l)$ .

Related Questions

Reena starts with a monthly salary of ₹8000 and gets an annual increment of ₹500. What will be her salary in the 10th year?

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

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