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Worked solution

Evaluate a finite geometric sum above ratio one

Find the sum of the first 1515 terms of a GP with first term a=0.6a=0.6 and common ratio r=1.5r=1.5.

CJC · Sequences and Series · Self-Practice 7

Answer

S15≈524S_{15}\approx524 (3 significant figures).

Compare your reasoning

Substitute the number of terms, not the final exponent

S15=0.6(1.515−1)1.5−1=4294841781920≈524.272668457≈524\begin{aligned}&S_{15}\\ & =\frac{0.6(1.5^{15}-1)}{1.5-1}\\ & =\frac{42948417}{81920}\approx524.272668457\approx524\end{aligned}

The printed answer is rounded to 524. This authored calculation keeps an exact fractional check before rounding.

How did this question go?

Common mistakes

A finite sum is valid for r>1; no sum-to-infinity assumption is needed. The printed 524 is not the exact total.