Evaluate the finite sum _ k=0 ^ 7 5 ( 3 2 )^ k

MATHEMATICS · Subjective · A Level · Mathematics · Sequences and series · Sequences and series

Problem

Evaluate the finite sum ∑k=075(32)k.\sum_{k=0}^{7} 5\left(\dfrac{3}{2}\right)^{k}. Present your solution in the following order: (i) identify the first term and common ratio, (ii) calculate the required sum, and (iii) state the exact numerical value obtained.

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