Question

Insert four Numbers between 8 and 26 so that the resulting sequence is an A.P(11th class Maths)

Answer 1

let the 4 no are a,a+d,a+2d,a+3d,a+4d
here,a=8
last term=26
a+(n-1)d=26
8+4d=26(since it has 5 term,so n=5
d=4.5
so numbers are 8 ,12.5 ,17 ,21.5 , 26

Answer 2

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Assume that A1, A2, A3, A4, and A5 are the five numbers between 8 and 26, such that the sequence of an A.P becomes 8, A1, A2, A3, A4, A5, 26

Here, a= 8, l =26, n= 5

Therefore, 26= 8+(7-1)d

Hence it becomes,

$\tt 26 = 8+6d$

$\tt 6d = 26-8 = 18$

$\tt 6d= 18$

$\tt d = 3$

$\tt A1= a+d = 8+ 3 =11$

$\tt A2= a+2d = 8+ 2(3) =8+6 = 14$

$\tt A3= a+3d = 8+ 3(3) =8+9 = 17$

$\tt A4= a+4d = 8+ 4(3) =8+12 = 20$

$\tt A5= a+5d = 8+ 5(3) =8+15 = 23$

Hence, the required five numbers between the number 8 and 26 are 11, 14, 17, 20, 23

Hope it's Helpful....:)