Question

Find the sum of each series, if it exists91 + 85 + 79 + … + (­29)

Answer 1

Answer:

651.

Step-by-step explanation:

Note: In the given series it should be -29 instead of 29 because 29 cannot be a term of AP whose first term is 91 and common difference is -6.

Consider the given series is

$91+85+79+...+(-29)$

It is the sum of an AP. Here,

First term = 91

Common difference = 85 - 91 = -6

Last term = -29

nth term of an AP is

$a_n=a+(n-1)d$

where, a is first term and d is common difference.

$-29=91+(n-1)(-6)$

$-29-91=(n-1)(-6)$

$\dfrac{-120}{-6}=(n-1)$

$20=(n-1)$

$n=20+1=21$

Sum of AP is

$Sum=\dfrac{n}{2}[\text{First term + Last term}]$

$Sum=\dfrac{21}{2}[91+(-29)]$

$Sum=\dfrac{21}{2}[62]$

$Sum=651$

Therefore, the sum of given series is 651.