The sum of all multiples of 7 between 0 and 500 is
(a) 13916
(b) 17892
(c) 24353
(d) 16984

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Solution

(b) 17892

The multiples of 7 between 0 and 500 are 7, 14, 21, 28, ..., 497.
This is an AP in which a = 7, d = (14 - 7) = 7.
Let the number of terms be n.
Then T_n = 497
⇒ a + (n - 1)d = 497
⇒ 7 + (n - 1) ⨯ 7 = 497
⇒ 7n = 497
⇒ n = 71

∴ S₁₇ = $\frac{n}{2} (a + l) = (\frac{71}{2}) \times (7 + 497) = 71 \times 252 = 17892$

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