Sn=-441 for the series 19 + 15 + 11 tn. determine the value of n.

(i’ve gotten as for as -441 = 21n - 2n^2, but i can’t seem to understand how to get to the next

The value of n is 21

Step-by-step explanation:

The series is 19 , 15 , 11 , ............

It has a constant difference between each two consecutive terms, so it is an arithmetic series.

The rule of the sum of n terms in the arithmetic series is:

Where a is the first term of the series , d is the difference between each two consecutive terms and n is the number of the terms in this series

So from the series above:

a = 19 , d = 15 - 19 = -4 ( it must be second term - first term ) ,

⇒Use factorization

(2n + 21) (n - 21) = 0

2n + 21 = 0 ⇒ 2n = -21 ⇒ n = -21/2⇒Not accepted n must be positive integer

n - 21 = 0⇒ n = 21

∴-441 is the sum of 21 terms in this series  

439400

step-by-step explanation:

130^2 = 16900

16900*26 = 439400

6

step-by-step explanation: