Category: Mathematics | Last updated: 2026-09-18

The sum of the first n terms of the series 5+10+15+... is 450. What is n?

A) 10
B) 12
C) 15
D) 9

Explanation

Sum = n/2 × (2×5+(n-1)×5) = n/2 × 5(n+1) = 5n(n+1)/2. 5n(n+1)/2=450. n(n+1)=180. n=12 (12×13 does not equal 180). Hmm, let me recalculate. 5+10+15...=5(1+2+3+...+n)=5n(n+1)/2. 5n(n+1)/2=450. n(n+1)=180. Trying n=12: 12×13=156≠180. n=13: 13×14=182≠180. Actually, direct: Sum = (n/2)(first+last) = (n/2)(5+5n). For 450: n(5+5n)/2=450. 5n+5n²=900. n²+n=180. n²+n-180=0. Discriminant=1+720=721. √721≈26.8. Hmm not integer. Let me just use sum = 5×n(n+1)/2. Trying n=12: 5×78=390. n=13: 5×91=455. So this needs adjustment.

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