3 years ago

Whats the difference between an exponent and a base?

Mathematics

1 answer:

Volgvan3 years ago

8 0

Answer:

Hey

Step-by-step explanation:

As nouns the difference between exponent and base is that exponent is one who expounds, represents or advocates while base is something from which other things extend; a foundation or base can be . As a verb base is to give as its foundation or starting point; to lay the foundation of. As a adjective base is (obsolete) low in height; short.

hope this helps!

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Given the sequence in the table below, determine the sigma notation of the sum for term 4 through term 15

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$a_n=5 \ for \ n=1 \\
a_n=-10 \ for \ n=2 \\
a_n=20 \ for \ n=3$

You can see it's a geometric sequence because the ratio is constant ( $\frac{a_3}{a_2}=\frac{a_2}{a_1}$ ).
The nth term of a geometric sequence:
$a_n=a_1 \times r^{n-1}$

$a_1=5 \\
r=\frac{a_2}{a_1}=\frac{-10}{5}=-2 \\ \\
a_n=5(-2)^{n-1}$

It has to be the sum for term 4 through term 15, so n=4 and the number above the sigma is 15.

Your answer:
$\sum^{15}_{n=4} 5(-2)^{n-1}$

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