Find the sum of the first 15 terms of each of the following sequences having nth term as$b_n = 5 + 2n$

Given:

nth term of an A.P. is given by $b_n = 5 + 2n$.

To do:

We have to find the sum of the first 15 terms.

Solution:

Here,

\( b_{n}=5+2 n \)

Number of terms \( =15 \)

\( b_{1}=5+2 \times 1=5+2=7 \)
\( b_{2}=5+2 \times 2=5+4=9 \)
\( \therefore \) First term \( (a)=7 \) and \( d=9-7=2 \)

We know that,
${S}_{n}=\frac{n}{2}[2 a+(n-1) d]$
\( \mathrm{S}_{15}=\frac{15}{2}[2 a+(15-1) d] \)
\( =\frac{15}{2}[2 \times 7+(15-1) \times 2] \)
\( =\frac{15}{2}[14+14 \times 2]=\frac{15}{2}[14+28] \)
\( =\frac{15}{2}+42=15 \times 21=315 \)

The sum of the first 15 terms is $315$.

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Updated on: 10-Oct-2022

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