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Vika [28.1K]
3 years ago
10

Find the sum of the first 30 terms of the sequence below an=3n+2

Mathematics
2 answers:
Solnce55 [7]3 years ago
6 0
First off, let's find the 1st term's value, and the 30th term's value,

\bf a1=3(1)+2\implies a1=5\qquad \qquad \quad   a30=3(30)+2\implies a30=92\\\\
-------------------------------\\\\
~~~~~~~\textit{ Sum of an arithmetic sequence}\\\\
S_n=\cfrac{n(a1+an)}{2}~ 
\begin{cases}
n=n^{th}\ term\\
a1=\textit{first term's value}\\
----------\\
a1=5\\
a30=92\\
n=30
\end{cases} \implies S_{30}=\cfrac{30(5+92)}{2}
\\\\\\
S_{30}=15(97)
prohojiy [21]3 years ago
4 0

Answer:

S_{30}= 1455.

Step-by-step explanation:

Given : an=3n+2.

To find : find the sum of the first 30 terms of the sequence.

Solution : We have given a_{n} = 3n + 2.

For first term n = 1

 a_{1} = 3 (1) +2.

a_{1} = 5

For last term n = 30

a_{30} = 3(30) +2

a_{30} = 90 +2

a_{30} = 92.

Then sum of first 30 terms

S_{30} =\frac{n(First\ term+last\ term)}{2}.

S_{30} =\frac{30(5+92)}{2}.

S_{30} =\frac{30(97)}{2}.

S_{30}= 15 *97.

S_{30}= 1455.

Therefore, S_{30}= 1455.

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