Question

Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

Answer 1

The five numbers have to be inserted between 8 and 26.

Let A 1 , A 2 , A 3 , A 4 , and A 5 be the five numbers, such that 8, A 1 , A 2 , A 3 , A 4 , A 5 ,26 are in an A.P.

The formula for the common difference while introducing arithmetic mean between two terms is given by,

d= b−a n+1 (1)

Here,

a=8 b=26 n=5

Substitute the values in equation (1).

d= 26−8 5+1 = 18 6 =3

The n numbers between 8 and 26 in the A.P. are given by,

A 1 =a+d

Substitute the values of a and d in the above expression,

A 1 =8+3 =11 A 2 =a+2d

Substitute the values of a and d in the above expression,

A 2 =8+2×3 =8+6 =14 A 3 =a+3d

Substitute the values of a and d in the above expression.

A 3 =8+3×3 =8+9 =17 A 4 =a+4d

Substitute the values of a and d in the above expression.

A 4 =3+4×3 =15 A 5 =a+5d

Substitute the values of a and d in the above expression.

A 5 =8+5×3 =8+15 =23

Thus, the five numbers between 8 and 26 are 11,14,17,20 and 23 respectively.