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
[tex]91+85+79+...+(-29)[/tex]
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
[tex]a_n=a+(n-1)d[/tex]
where, a is first term and d is common difference.
[tex]-29=91+(n-1)(-6)[/tex]
[tex]-29-91=(n-1)(-6)[/tex]
[tex]\dfrac{-120}{-6}=(n-1)[/tex]
[tex]20=(n-1)[/tex]
[tex]n=20+1=21[/tex]
Sum of AP is
[tex]Sum=\dfrac{n}{2}[\text{First term + Last term}][/tex]
[tex]Sum=\dfrac{21}{2}[91+(-29)][/tex]
[tex]Sum=\dfrac{21}{2}[62][/tex]
[tex]Sum=651[/tex]
Therefore, the sum of given series is 651.
