Question

Consider the arithmetic series:

3 + 8 + 13 + 18 + ... + (5n - 2) + ...

Write a formula for the sum of the first n terms in this series.

Answer 1

\[\bf S_{n}=\frac{n}{2}\left( 2a+(n-1)d \right)\], Now replace d with the common difference of the sequence and a with the first term and that you gives you the general term for the sum of the first n terms.

Answer 2

For us, d = 5 and a = 3. Replacing d and a with these values will give you the the formula for the sum of the first n terms.

Answer 3

o-o?

Answer 4

S denotes the sum. The formula for the sum of the first n terms of an arithmetic series is given by the formula:\[\bf S=\frac{ n }{ 2 }(2a+(n-1)d)\]Where S is the sum of the first n terms, a is the first term of the series, and the d is the common difference.