Chapter 12.2, Problem 41AYU

In Problems 39-56, find each sum.

$2+4+6+\cdots +70$

To determine

To find: The sum of the given sequence.

Answer to Problem 41AYU

$1260$

Explanation of Solution

Given:

$2+4+6+\dots +70$

Formula Used:

If $a_1,a_n$ and $d$ are known, then $n$^th term can be found by the formula,

$a_n=a_1+\left(n-1\right)d$   (Formula 1)

Sum of the first $n$ terms of an arithmetic sequence.

$S_n=\frac{n}{2}\left[a_1+a_n\right]$   (Formula 2)

Calculation:

To find $n$:

From the given sequence, $a_1=2,a_n=70\text{ and }d=2$.

$70=2+\left(n-1\right)2=2+2n-2=2n$   ( By Formula 1)

$\Rightarrow n=35$

To find the sum $S_{35}$:

$S_{35}=\frac{35}{2}\left[2+70\right]=35\times 36=1260$   (By Formula 2)