(K:1) Find S8 for the series 3+15+75+375+…

Question

BlackTom AI · Accepted Answer

The series 3, 15, 75, 375, … is a geometric progression with first term a1 = 3 and common ratio r = 5. To find S8 (the sum of the first 8 terms), use the geometric series sum formula: S_n = a1 * (r^n − 1) / (r − 1).

Compute r^n: 5^8 = 390,625.
Subtract 1: 390,625 − 1 = 390,624.
Multiply by a1: 3 * 390,624 = 1,171,872.
Divide by (r − 1): 1,171,872 / 4 = 292,968.

Thus S8 = 292,968. Now evaluate each option:

Option a: 724. This is far too small for a sum that grows by a factor of 5 each term; it does not reflect the rapid growth of the sequence.

Option b: 38. This value is also far too small and does not account for the repeated multiplication by 5 across eight terms.

Option c: 292,968. This matches the correct calculation from the geometric sum formula and aligns with the sequence’s rapid growth.

Option d: 97,656. This is smaller than the true sum; it might correspond to summing fewer terms or missing a factor, but it does not equal the eight-term sum.

In short, recognizing the pattern as a geometric progression and applying the sum formula yields the correct total, while the other numbers fail to reflect the compounded growth across eight terms.

(K:1) Find S8 for the series 3+15+75+375+…

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