Find the sum to $n$ term of the A.P. $5, 2, -1, -4, -7, …,$

Given:

Given A.P. is $5, 2, -1, -4, -7, …,$

To do:

We have to find the sum to $n$ term of the A.P. $5, 2, -1, -4, -7, …,$

Solution:

Here,

\( a=5, d=2-5=-3 \) and \( n=36 \)

We know that,

\( S_{n}=\frac{n}{2}[2 a+(n-1) d] \)
\( \therefore S_{n}=\frac{n}{2}[2 \times(5)+(n-1) \times -3] \)
\( =\frac{n}{2}[10-3n+3] \)
\( =\frac{n}{2}[13-3n] \)

The sum of the given A.P. to $n$ terms is $\frac{n}{2}[13-3n]$.

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Updated on: 10-Oct-2022

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