Question

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

Answer 1

Answer:

-223948 is the sum of 7 terms.

Step-by-step 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 = $a.\frac{r^{n}-1 }{(1-r)}$

sum = $(-4).\frac{6^{7}-1 }{6-1}=(-4).\frac{(279936-1)}{(6-1)}=(-4).\frac{279935}{5}=(-4).55987=-223948$

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