Correct Answer - Option 2 : n
2
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