Question

Which term of the A.P. -2,-7,-12, ... will be equal to -77? Find the sum of the terms upto -77.

• A. -632
• B. -630
• C. -627
• D. -615

Answer 1

The correct option is A -632

First term, a = -2
Common difference, d = -7-(-2) = -5

$n^{th}$ term of an AP = a + (n-1)d

$\Rightarrow$ -77 = -2 + (n -1) (-5)
$\Rightarrow$ -77 = -2 - 5n + 5
$\Rightarrow$ -80 = -5n
$\Rightarrow$ n = 16

Therefore -77 is the ${16}^{th}$ term of the AP.

Sum of first n terms of an AP
$=\frac{n}{2}(a+l)$

We found that -77 is the ${16}^{th}$ term of the AP.

$\therefore$ Sum of the terms upto -77 = Sum of first 16 terms.

$=\frac{16}{2}(-2+(-77\left)\right)$

$=8(-2-77)$

$=8(-79)$

$=-632$

$\therefore$ Sum of the terms upto -77 = -632