Question

Find the sum of a finite geometric sequence from n = 1 to n = 7, using the expression −4(6)^n − 1.

a. 111,325
b. 526
c. 782
d. -22,948

Answer 1

-223948 is the sum of 7 terms.

Explanation:

The given geometric sequence is in the form of
`T_(n)=-4.6^(n)-1`

Therefore the sequence will be -25, -145, -865........(n =7)

Therefore sum of the seven terms =
`a.(r^(n)-1 )/((1-r))`

sum =
`(-4).(6^(7)-1 )/(6-1)=(-4).((279936-1))/((6-1))=(-4).(279935)/(5)=(-4).55987=-223948`

Sum of seven terms will be = -223948

Answer 2

Now we know what the common ratio is, 6, and what the first term is, -4,
and our nth term is 7, since we're asked to do the sum
from 1 to 7.
S7= - 4(1-6(7)/(1-6))
=-223948