Find the sum of $n$ terms of an A.P. whose nth terms is given by $a_n = 5 – 6n$.

Given:

nth terms of an A.P. is given by $a_n = 5 – 6n$.

To do:

We have to find the sum of the given A.P. to $n$ terms.
Solution:

\( n^{\text {th }} \) term of the given A.P. is \( a_{n}=5-6 n \).
First term \( =a_{1}=5-6 \times 1=5-6=-1 \)
\( a_{2}=5-6 \times 2=5-12=-7 \)
\( \therefore d=a_{2}-a_{1}=-7-(-1)=-7+1=-6 \)
\( \therefore \mathrm{S}_{n}=\frac{n}{2}[2 a+(n-1) d] \)
\( =\frac{n}{2}[2 \times \dot{(-1)}+(n-1)(-6)] \)
\( =\frac{n}{2}[-2-6 n+6]=\frac{n}{2}[4-6 n] \)
\( =\frac{n}{2} \times 2[2-3 n]=n(2-3 n) \)

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Updated on: 10-Oct-2022

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