Question

The sum of the first 120 terms of the sequence 14, 16, 18, 20...…

Short answer

The sum of the first 120 terms of the Arithmetic sequence is 15960

Step-by-step solution

Given information 

Arithmetic sequence 14, 16, 18, 20...…

we need to find sum of first 120 terms

Sum 

The formula to find out sum is

$$\begin{gathered} S_n=\frac{n}{2}\left(2a_1+(n-1)d\right) \\ where{a}_{1}isthefirstterm \\ disthedifferencebetweentheterms \\ nisthenumberofterms \end{gathered}$$

common difference 

given arithmetic sequence is 14,16,18, 20,....

common difference d= 16-14=2

first term is 14.

we need to find out sum of 120 terms, so n=12

Sum 

Substitute all the values and find out sum

$$\begin{gathered} S_n=\frac{n}{2}\left(2a_1+(n-1)d\right) \\ {S}_{120}=\frac{120}{2}\left(2\left(14\right)+(120-1)2\right) \\ {S}_{120}=60\left(28+238\right) \\ {S}_{120}=15960 \\ Sumoffirst120terms=15960 \end{gathered}$$