Question

20 A.Ms are inserted between 2 and 86. Find the 19th A.M.

Answer 1

When we add 20 A.Ms between 2 and 86, the resultant AP would look like
$2,A_1,A_2,........A_{19},A_{20},86$

There are 22 numbers in this AP including 2 and 86.
First term of this AP is 2 and the last term is 86. $A_1$ is the second term and 86 is the ${22}^{nd}$ term.
$t_1=2$
$t_{22}=86$
To find the common difference,
2 + (22-1)d = 86
d = 4
$A_{19}$ is the ${20}^{th}$ term of the AP
$A_{19}=t_{20}$
$t_{20}$ = 2 + (20-1)4
$=2+19\times 4$
$=78$