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A geometric series has a sum of 1365. Each item increases by a factor of 4. If there
are 6 terms in the series, find the value of the first term.

Sagot :

edisonlara1212

Answer:

1

Step-by-step explanation:

So the sum of a finite geometric series can be defined as: [tex]S_n = \frac{a_1-a1*r^n}{1-r}[/tex] where r is the constant ratio or how much more greater the current term is, compared to the previous term (how much it's being multiplied by), and the n is the number of terms in the series. So with the given information you have the equation:

[tex]1365=\frac{a_1-a_1*4^6}{1-4}[/tex]

Simplify:

[tex]1365=\frac{a_1-4096a_1}{-3}[/tex]

Multiply both sides by -3

[tex]-4095 = a_1-4096a_1[/tex]

Subtract coefficients

[tex]-4095=-4095a_1[/tex]

Divide both sides by -4095

[tex]1 = a_1[/tex]

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