Question

Assertion :The sum of the series with the $nth$ term, $t_n=(9-5n)$ is $-465$,

when no. of terms $n=15$.

Reason: Given series is in A.P. and sum of $n$ terms of an A.P. is $S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

When $n=1$ then $t_1=4$
when $n=15$ then $t_{15}=-66$
Sum $S_n=\frac{n}{2}(a+l)$
$\therefore S_{15}=\frac{15}{2}(4-66)$
= $-465$
The assertion and reason are both correct and reason is the correct explanation of the assertion.