Find the sum of the first 10 terms in the sequence using the appropriate formula. Show the formula and the steps used to get your answer

Question

Find the sum of the first 10 terms in the sequence using the appropriate formula. Show the formula and the steps used to get your answer

5,-20,80,-320

r= -4

Answer 1

Sn = a1(1-r^n)/(1-r) as long as r doesn't =1. r = common ratio. n= number of term S =sum of the geometric series

Sn = sum of the n terms of the geometric series.

n=10

r=-r = an+1/an = a2/a1 = -20/5 = 80/-20 = -4

Sn = a1(1-r^n)/(1-r)

Sn = 5[(1-(-4)^10)]/(1--4 )

Sn = 5([1-1,048,576)]/5

Sn = -1,048,575

they alternate in sign, with odd terms positive

10 is even, so the sum must be negative

here's the 1st ten terms

5, -20, 80, -320, 1,280, - 5,120, 20,480, -81,920, 327,680,-1,310,720, ...

sum is definitely negative as the last term dominates, but less than the last term

sum= -1,048,575

Sn = a little less than negative one million

Answer 2

desmos.com/calculator/ithvwxkmzu