Question

Which summation formula represents the series below?

13 + 9 + 5 + 1

Answer 1

The summation formula for the series is ⇒ 15n - 2n²

Explanation:

* Lets check the series 13 , 9 , 5 , 1

∵ 9 - 13 = -4

∵ 5 - 9 = -4

∵ 1 - 5 = -4

∴ The series has a common difference

∴ It is an arithmetic series with first term a and constant difference d

* That means

- a1 = a , a2 = a + d , a3 = a + 2d , a4 = a + 3d

∴ an = a + (n - 1)d, where n is the position of the number in the series

* The sum of the arithmetic series can find by the rule

- Sn = n/2[2a + (n - 1)d], where n is the number of terms you want to add

* Lets use this rule in our problem

∵ Sn = n/2[2(13) + (n - 1)(-4)]

∴ Sn = n/2(26 + (-4n + 4)] ⇒ open the small bracket

∴ Sn = n/2[26 - 4n + 4] ⇒collect the like terms

∴ Sn = n/2[30 - 4n] ⇒ open the bracket

∴ Sn = (n/2)(30) - (n/2)(4n)

∴ Sn = 15n - 2n²

* The summation formula for the series is 15n - 2n²

Answer 2

The summation that represents this series is:

∑ (13-4(n-1))

Explanation:

The first term of the series is 13=13-4×0

Second term=9=13-4=13-4×1

third term=5=13-4-4=13-4×2

fourth term=1=13-4-4-4=13-4×3

Hence, the nth term of this series will be:

an= 13-4(n-1) ;n=1,2,3,...

Hence, the summation that represents this series is:

∑ (13-4(n-1))