Question

20 A.Ms are inserted between 2 and 86. The value of 19th A.M. is .

• A. 78
• B. 84
• C. 82
• D. 80

Answer 1

The correct option is A 78

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

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