Question

3. Given the geometric series 300 +360+432 +518.4+, what is the sum of the first 10 terms?
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Answer 1

The sum of the first 10 terms of the given geometric series 300 +360+432 +518.4+..... is 7787.60.

What is the sum of terms of a geometric sequence?

Let's suppose its initial term is  a , the multiplication factor is  r

and let it has total n terms, then, its sum is given as:

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

(sum till nth term)

For the given geometric series, the common ratio is,

r = (360/300) = 1.2

Also, the first term of the series is 300. Therefore, the sum of the first ten terms of the series are:

Sum = a(rⁿ-1)/(r-1) = 300(1.2¹⁰-1)/(1.2-1) = 300(5.1917)/0.2 = 7787.60

Hence, the sum of the first 10 terms of the given geometric series is 7787.60.

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