Question

Observe the pattern given below,

The sum of terms up to $n^{th}$ position will be given by the expression:

• A. $\frac{n(n+1)}{2}$
• B. $\frac{n(n-1)}{2}$
• C. $n(n-1)$
• D. $n^2$

Answer 1

The correct option is A

$\frac{n(n+1)}{2}$

Let S = 1 + 2 + 3 +.............. + (n-1) + n [Eqn.1]

S = n + (n-1) + (n-2) + ........... + 2 + 1 [Eqn.2]

Adding Eqn.1 and 2, we get,

2S = (n+1) + (n+1) + (n+1) + (n+1) + ........... + (n+1)

Here, (n+1) is added 'n' times

2S = n × (n+1)

S= $\frac{n(n+1)}{2}$