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Mathematics

Find the sum of first 12 natural numbers each of which is a multiple of 7.

AP

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Answer

First 12 natural numbers that are a multiple of 7 are,

7, 14, 21, ……….., 12th term.

The above sequence is an A.P. with a = 7 and common difference = 7.

S=n2(2a+(n1)d)=122(2×7+(121)×7)=6(14+77)=6×91=546.S = \dfrac{n}{2}(2a + (n - 1)d) \\[1em] = \dfrac{12}{2}(2 \times 7 + (12 - 1) \times 7) \\[1em] = 6(14 + 77) \\[1em] = 6 \times 91 \\[1em] = 546.

Hence, sum of first 12 natural numbers that are divisible by 7 is 546.

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