Question

insert four number between 8and 26so that the result sequence is an A.p

Answer 1

a=8
An=a+(n-1)d
n=4
An=26
26=8+(4-1)d
26=8+3d
26-8=3d
18=3d
6=d
a1=8
a2=a+d=8+6=14
a3=a+2d=8+2(6)=8+12=20
a4=a+3d=8+3(6)=8+18=26

Answer 2

Let A1, A2, A3, A4, and A5 be five numbers between 8 and 26 such that
8, A1, A2, A3, A4, A5, 26 is an A.P.
Here, a = 8, b = 26, n = 7
Therefore, 26 = 8 + (7 – 1) d
⇒ 6d = 26 – 8 = 18
⇒ d = 3
A1 = a + d = 8 + 3 = 11
A2 = a + 2d = 8 + 2 × 3 = 8 + 6 = 14
A3 = a + 3d = 8 + 3 × 3 = 8 + 9 = 17
A4 = a + 4d = 8 + 4 × 3 = 8 + 12 = 20
A5 = a + 5d = 8 + 5 × 3 = 8 + 15 = 23
Thus, the required five numbers between 8 and 26 are 11, 14, 17, 20, and 23.