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:

-Dominant- [34]2 years ago

8 0

Answer:

Sum of the geometric sequence is 19662.

Step-by-step explanation:

Sum of the terms in a geometric series is represented by the formula

$s_{n}=a\frac{(1-r^{n}) }{1-r}$

In this formula a = first term

r = common ratio

n = number of terms

Given in the question

a = 6

r = (-4)

n = 7

$S_{7}=(6)\frac{[1-(-4)^{7}] }{[1-(-4)]}=6.\frac{(1+16384)}{(1+4)}=\frac{(6)(16385)}{5}= 19662$

Therefore sum of the sequence is 19662

xxMikexx [17]2 years ago

3 0

The shortest way is to use the sum formula for GP

S =a(1-rⁿ) /(1-r)

a=6

r=(-4)

n=7 (seventh term) ===> S=6(1-(- 4)⁷)/[1- -4)] =19,662

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krek1111 [17]

Since the perimeter must not exceed 291.
Let the third side be x.

x + 87 + 64 < 291
x + 151 < 291.
x < 291 -151.
x < 140. (First)

But for a triangle there is what is called the Triangle Inequality Theorem. That given the two sides of a tringle, the third side of the triangle must greater than the positive difference between the two sides and less than the sum of the two sides.

So for this case. 87 and 64.

x > ( 87 - 64). x > 23.
x < (87 + 64) x < 151. Combine both inequalities.

23 < x < 151 (second).

Combining First and second. Both must be satisfied.
So we have a more accurate answer as:

23 < x < 140. x is greater than 23 and x is less than 140.

x could be 24, 25, 26, 27, ......, 139. cm.

I hope this helps.

3 0

3 years ago

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Verdich [7]

Answer:

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