Which summation formula represents the series below? 13 + 9 + 5 + 1

Mathematics

2 answers:

Leona [12.6K]2 months ago

8 0

Answer:

$\sum_{x=1}^{4}(17-4n)$

Step-by-step explanation:

The expression in question is

$13+9+5+1$

The series consists of the following terms

13,9,5,1

This is an arithmetic progression (AP). The first term here is 13, and the common difference is -4.

The nth term formula for an AP is

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

where a represents the first term and d is the common difference.

The nth term of the AP defined here is

$a_n=13+(n-1)(-4)$

$a_n=13-4n+4$

$a_n=17-4n$

The formula for summation of an AP is

$\sum_{x=1}^{n}a_n$

The total number of terms is 4, thus, the summation formula can be stated as

$\sum_{x=1}^{4}(17-4n)$

AnnZ [12.3K]2 months ago

5 0

$13 + 9 + 5 + 1 = 27$

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