Question

Can you get the answer and explain how you did it, i am really struggling right now

Answer 1

9514 1404 393

Answer:

453.32

Explanation:

The argument of the summation symbol is recognizable as the general term of a geometric series with first term a1=4 and common ratio r=1.5. The indices on the summation symbol tell you that you want the sum of the first 10 terms of the series.

The general form of the sum of the first n terms of a geometric series is ...

Sn = a1(r^n -1)/(r -1)

For the given values of a1 and r, this sum is ...

`S_(10)=4\cdot(1.5^(10)-1)/(1.5-1)=4\cdot(57.6650390625-1)/(0.5)\\\\\boxed{S_(10)\approx453.32}`

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Your graphing calculator may be able to evaluate this for you directly.