Class 11

Math

Algebra

Sequences and Series

If $6$ arithmetic means are inserted between $1$ and $29 $, then find the $4_{th}$ arithmetic mean.

$⇒1,a_{1},a_{2},.....,a_{6},9/2$ will be in A.P.

Now,

$n_{th}$ term $a_{n}=a+(n−1)d$

$8_{th}$ term

$29 =1+7d⇒27 =7d⇒d=21 $.

Hence

$4_{th}$ term

$a_{4}=1+4(21 )=3$.