230k views
4 votes
Sum of the arithmetic sequence- Find each sum: 5+ 9 +13 + ... +49

User Waldelb
by
8.4k points

1 Answer

5 votes

ANSWER

324

Step-by-step 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=(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=(48)/(4) \\ n=12 \end{gathered}

There are 12 terms.

Therefore:


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

That is the sum of all the terms.

User Weiy
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories