Question

In an arithmetic progression the third term is four times the first term, and the sixth term is $17$, then ${20}^{th}$ term of the progression is

• A. $57$
• B. $59$
• C. $61$
• D. None of these

Answer 1

The correct option is B $59$

Let $a,d$ be the first term and the common difference of the A.P.

Then the third term is $a+(3-1)d=a+2d$.

According to the problem,

$a+2d=4a$

or $3a=2d$

or, $a=\frac{2d}{3}$......(1).

Also given the sixth term is $17$.

Then,

$a+5d=17$

or, $\frac{17d}{3}=17$ [Using (1)]

or, $d=3\Rightarrow a=2$.......(2).

Now the $20$ th term of the A.P. is

$=a+19d$

$=2+57=59$ [ Using (2)]