Question

What is the sum of a 6-term geometric series if the first term is 22 and the last term is 369,754?

Answer 1

AND
what is the sum of an 8 term geometric series id the first term is 15 and the last term is -4,199,040?

Answer 2

What is the sum of a 6–term geometric series if the first term is 22
and the last term is 369,754?

first term, a = 22
last term = 369,754

the general form of a geometric sequence is
a , a r , a r ² , a r ³ , .......... , a r ⁿ
.................>>>...where a is the first term,
.................>>>...r is the common ratio,
.................>>>...nth term = a r ^ ( n - 1 )

last term or 6th term = ar^5 = 369,754
( 22 ) r^5 = 369,754
r^5 = 16,807
r = 7
≈≈≈≈≈≈

sum of the 6-term geometric series is:
n
Σ a r^k = a ( 1 - r^(n+1)) / ( 1 - r )
k=0

5
Σ 22 ( 7 )^k = 22 ( 1 - ( 7 )^(5+1)) / ( 1 - 7 )
k=0
....................= 22 ( 1 - ( 7 )^6 ) / –6
....................= 22 ( 1 - 117,649 ) / –6
....................= 22 ( –117,648 ) / –6
....................= –2,588,256 / –6
....................= 431,376

Answer 3

Did that help?

Answer 4

oh my goodness, this is amazing! Thank you so much.

Answer 5

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Answer 6

Please.

Answer 7

will do!