Find the sum of each arithmetic series \sum_{n=1}^{13}\left(3n+

vetrila10

vetrila10

Answered question

2021-11-17

Find the sum of each arithmetic series
n=113(3n+5)

Answer & Explanation

Coon2000

Coon2000

Beginner2021-11-18Added 15 answers

Step 1
Given:
n=113(3n+5)
Substituting the value of n=1,2,3., we get
n=113(3n+5)=(3×1+5)=8
n=113(3n+5)=(3×2+5)=11
n=113(3n+5)=(3×3+5)=14
n=113(3n+5)=(3×4+5)=17
The arithmetic series is given as
n=113(3n+5)=8+11+14+17+. upto 13th term
Step 2
The first term of the arithmetic series is a=8.
The total number of term of the arithmetic series are n=13.
The common difference is given as
d=118=3
Step 3
The sum of the arithmetic series is given as
S=n2[2a+(n1)d]
Substituting the values, we get
S=132[2×8+(131)3]
S=132[16+(12)3]
S=132[16+36]
S=132×52
S=13×26
S=338
Hence, the sum of the series is 338.
Jeffrey Jordon

Jeffrey Jordon

Expert2022-08-30Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?