Answer:
The summation formula for the series is ⇒ 15n - 2n²
Step-by-step 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 <em>a</em> and constant difference <em>d</em>
* That means
- a1 = a , a2 = a + d , a3 = a + 2d , a4 = a + 3d
∴ an = a + (n - 1)d, where <em>n</em> 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 <em>n</em> 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
