Question

The average of 15 consecutive integers is 15. What is the smallest of the 15 integers?

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Answer 1

Step-by-step explanation:

Consider this as an arithmetic progression.

let a be the first term and d the common difference.

Since the question says consecutive integers which mean d = 1.

Average of 15 consecutive integers=( sum of the integers)/15(no. of integers)

here,

sum of the integers/15=15

sum of the integers =225 ------(1)

now using the formula for the sum of the arithmetic progression,

let s be the sum then,

s=[ (n) {2a + (n-1)d } ] \2 (here, n=15)

s=[15*(2a +14 ) ] \2 ------(2)

now equating (1) & (2), we get

[15*(2a +14 ) ] \2= 225

2a+ 14= 30

a = 8

which is the first term and the smallest term.

Answer is 8