Question

If the nth term of an A.P be (2n − 1), then the sum of its first n terms will be
1. n² - 1
2. (2n - 1)²
3. n²
4. n2 + 1

Answer 1

Correct Answer - Option 3 : n²

Concept:

The sum of n terms of an AP with first term a and common difference d is given by:

\(\rm S_n= \frac{n}{2}×(a+l)\)  or  \(\rm S_n= \frac{n}{2}×\left [ 2a+(n-l) d\right ]\)

Where l is the last term of the AP

Calculation:

Given that,

_Tn = 2n - 1   ----(1)

Put n = 1, 2, 3,... on equation (1), we will get first, second, third...term equals to 1, 3, 5,... respectively. 

Therrefore, 

a = 1, d = 2 

Hence, sum of n terms will be

\(\rm S_n= \frac{n}{2}×\left [ 2a+(n-l)2 \right ]\)

⇒ \(\rm S_n= \frac{n}{2}×\left [ 2.1+(n-l).2 \right ]\)

∴ S_n = n²