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FinnZ [79.3K]
3 years ago
11

What is the sum of a 7-term geometric series if the first term is -6, the last term is -24,576, and the common ratio is 4?

Mathematics
2 answers:
Zolol [24]3 years ago
7 0

Answer:  The required sum of the given geometric series is - 32766.

Step-by-step explanation:  We are given to find the sum of a 7-term geometric series if the first term is -6, the last term is -24,576 and the common ratio is 4.

We know that,

if 'a' is the first term and 'r' is the common ratio of a geometric series, then its sum up to n terms is given by

S_n=\dfrac{a(1-r^n)}{1-r},~r1.

In the given geometric series,

first term, a = -6  and  common ratio, r = 4.

Since r = 4 > 1, so the sum up to 7 terms is

S_7\\\\\\=\dfrac{a(r^7-1)}{r-1}\\\\\\=\dfrac{-6(4^7-1)}{4-1}\\\\\\=\dfrac{-6(16384-1)}{3}\\\\\\=-2\times 16383\\\\=-32766.

Thus, the required sum of the given geometric series is - 32766.

Zanzabum3 years ago
3 0
<h3><u>Answer:</u></h3>

Hence, the sum of a 7-term geometric series is:

-32766.

<h3><u>Step-by-step explanation:</u></h3>

We have to find the sum of a 7-term geometric series (i.e. n=7) if the first term(a) is -6, the last term is -24,576, and the common ratio(r) is 4.

We know that the sum of the 7-term geometric series is given as:

S_n=a\times (\dfrac{r^n-1}{r-1})

On putting the value of a,n and r in the given formula we have:

S_7=(-6)\times (\dfrac{4^7-1}{4-1})\\\\\\S_7=-32766

Hence, the sum of a 7-term geometric series is:

-32766.

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