Question

Find the sum of all the non-negative terms of the following sequence: 100, 97, 94, ….

• A. 1717
• B. 1719
• C. 1721
• D. 1723

Answer 1

The correct option is A

1717

Here, $t_1$ = 100, common difference, d = $t_2$ – $t_1$ = 97 – 100 = -3

$t_n$ = $t_1$ + (n-1)d $\Rightarrow$100 + (n-1)(-3) = 100 – 3(n-1) = 103 – 3n.

Let $t_n$ be the first negative term. i.e,

$t_n$ < 0 $\Rightarrow$ 103 - 3n < 0 $\Rightarrow$ n > $\frac{103}{3}$ > 34

That is, the ${35}^{th}$ term will be negative.

Sum of the first $34$ terms = ( $\frac{34}{2}$)(first term + last term)

= $17(100+100+(34-1\left)\right(-3\left)\right)=1717$