Question

There is a sequence of 11 consecutive odd numbers if the average of first 7 number is x then find the average of all the 11 integers

Answer 1

Answer:

(x+4)

Step-by-step explanation:

Consecutive odd numbers will be in Arithmetic Progression whose common difference d= 2

let the numbers be a1, a2,........,a11

given - (a1+a2+.....+a7)/7 = x

sum of AP = N/2(a1 + aN)

where N is total terms

a1 first term

Now apply the Sum formula for the first seven terms

7x = 7/2(a1+a7)

a1+a7= 2x

we can write

a7= a1 + 6d

a7 = a1 + 12 put this in the equation

2a1 + 12= 2x

a1= x-6

a11 = a1 +10d= x +14

Now the sum of 11 terms will be

S = 11/2( a1 + a11)

S = 11/2( 2x + 8)

S= 11(x+4)

now the average of 11 terma will be their sum divided by 11

average will come to (x+4)