Question

The sum of n consecutive natural even numbers starting from 6 is 84. Find the n value.

Answer 1

This can be solved using Arithmetic Progression Concept.

let there be a AP- 6,8,10,12,14.....R which has n terms.

R is the nth term.

nth term of AP= First Term + (n-1)Common Difference

R= 6+ (n-1)2

R= 6+ 2n- 2

R= 4 + 2n------------------①

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Sum of n  term in AP= (FIRST TERM + LAST TERM )(NUMBER OF TERMS /2)

84= (6 + R) n/2

84= (6 + 4+2n) n/2

168 = 10n +2n²

10n +2n² -168=0

n²+5n -84=0

on solving we get n=7