Question

Sum of the arithmetic sequence- Find each sum: 5+ 9 +13 + ... +49

Answer 1

ANSWER

324

EXPLANATION

We want to find the sum of the arithmetic progression:

$5+9+13\ldots_{}+49$

To do that we apply the formula for the sum of an arithmetic sequence:

$S_n=\frac{n}{2}(a+l)$

where a = first term

l = last term

n = number of terms

We have to find n by using the last term:

$a_n=a+(n-1)d$

d = common difference

The common difference is 4. Therefore, we have to find n:

$\begin{gathered} 49=5+(n-1)\cdot4 \\ 49=5+4n-4 \\ 49=1+4n \\ \Rightarrow4n=49-1=48 \\ n=\frac{48}{4} \\ n=12 \end{gathered}$

There are 12 terms.

Therefore:

$\begin{gathered} S_n=\frac{12}{2}(5+49)=6\cdot(54) \\ S_n=324 \end{gathered}$

That is the sum of all the terms.