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In an AP  1, 3, 5,... find the sum of n terms ?
1. n
2. n2
3. 2n - 1
4. n3

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Correct Answer - Option 2 : n2

Concept:

Let us consider sequence a1, a2, a3 …. an is an A.P.

  • Common difference “d”= a2 – a1 = a3 – a2 = …. = an – an – 1
  • nth term of the A.P. is given by an = a + (n – 1) d
  • Sum of the first n terms = \(\rm S_n= \frac{n}{2}[2a+(n-1)\times d]\) = \(\rm\frac{n}{2}[a+l]\)

Where, a = First term, d = Common difference, n = number of terms, an = nth term and l = Last term

Calculation:

Given sequence are 1, 3, 5,... 

a = 1 , d = 2 then Sn =?

As we know, \(\rm S_n= \frac{n}{2}[2a+(n-1)\times d]\)

\(\rm = \frac{n}{2}[2 \times +(n-1)\times 2]\)

= n2

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