Beginning with 2, how many consecutive even numbers must be added to obtain a su...

October 2022 2 0 Report

Beginning with 2, how many consecutive even numbers must be added to obtain a sum of 42 ? *

ANSWER

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Beginning with 2, how many consecutive even numbers must be added to obtain a sum of 42?

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These even numbers of consecutive even numbers can forman arithmetic sequence.

And it's general form is:

an=2n { n represents the nth even numbers }

The sum of the first n terms is:

$\tt Sn= \frac{(a1 + an)•n}{2}$

$\tt 42= \frac{(2+2n)•n}{2}$

$\tt 42 = \frac{2(1 + n)n}{2}$

$\tt n(n+1)=42$

$\tt n²+n-42=0$

$\tt (n-6)(n+7)=0$

$\tt For \: n ≥ 1 \: and \: n \: is \: an \: integer$

$\tt \: So \: \: n=6$

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6 consecutive even numbers must be added to obtain a sum of 42.

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