Question

If there are eight arithmetic means inserted between the numbers $7$ and $43$, then, the fourth arithmetic mean from $43$ is $\square$.

Answer 1

$8$ arithmetic means are inserted between $7$ and $43$.

So $7,a_1,a_2,a_3,a_4,a_5,a_6,a_7,a_8,43$ are in A.P

$T_{10}=43and{T}_1=7d=\frac{43-7}{9}=4$

Now the fourth arithmetic mean from $43$ is $a_5$ which is basically the sixth term of the series.

$T_6=7+(6-1)\times 4=27$