Class 11

Math

Algebra

Sequences and Series

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

be five numbers between $8$ and $26$ such that $8,A_{1},A_{2},A_{3},A_{4},A_{5},26$ are in A.P.

Here, $a=8,b=26,n=7$

Therefore,$26=8+(7−1)d⇒6d=26−8=18⇒d=3$

$∴A_{1}=a+d=8+3=11A_{2}=a+2d=8+2×3=8+6=14A_{3}=a+3d=8+3×3=8+9=17A_{4}=a+4d=8+4×3=8+12=20A_{5}=a+5d=8+5×3=8+15=23$

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