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3 years ago

What is the sum of the first five terms of the geometric series 3 − 6 + 12 − . . . ?

Mathematics

1 answer:

mezya [45]3 years ago

5 0

3,−6,12,−24,...

You can rewrite this as:

(−1)n3⋅(1,2,4,8,...)

If we focus on 1,2,4,8...

an+1=2an
with a0=1.

This can be written out as a nice sum:
N∑n=02n=20+21+22+23+...
=1+2+4+8+...

Thus, now we can recombine everything to get:

3N∑n=0(−1)n2n

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steposvetlana [31]

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Step-by-step explanation:

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3 years ago

Use the the triangle.

KATRIN_1 [288]

For a 45 45 90 triangle if the legs are x length then the hyptonuse is x√2

a.
7=x
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b.
sin(45°)=(√2)/2

c.
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3 years ago

You deposit $500 in an account that pays 8% annual interest compounded yearly. What is the account balance after six years? Form

Diano4ka-milaya [45]

Principal, P = $500
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n = 1, the compounding interval
t = 6 years

The value after 6 years is
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That is,
A = $500*(1 + 0.08)⁶ = $793.44

Answer: $793.44

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3 years ago