Question

Find the sum of first n terms of an AP Whose nth term is (5-6n). Hence, find hte sum of its first 20 terms.

Answer 1

Given the general term is = 5-6n

So, 1st term = 5 - 6(1) = -1,

2nd term = 5 - 6(2) = -7

3rd term = 5 - 6(3) = -13

Hence the AP would be -1,-7,-13,-19,......$a_n$. with the first term, a = -1 and common difference d=-6.

Sum of n terms, $S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

$=\frac{n}{2}\left[2\right(-1)+(n-1\left)\right(-6\left)\right]$

$=\left(\frac{n}{2}\right)(4-6n)$

$=n(2-3n)$

$=2n-3n^2$ = sum of fjrst n terms

now putting n = 20 in above result we get the sum of first 20 terms

$S_{20}=2\left(20\right)-3(20\times 20)=40-1200=-1160$

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