Question

If $x+1,3x$ and $4x+2$ are the first three terms of an AP, then its $5^{\text{th}}$ term is ___.
(2 Marks)

Answer 1

Given, $x+1,3x,4x+2$ are in AP.
So, the difference of any two consecutive terms will be the same.

$\therefore 3x–(x+1)=(4x+2)–3x$
$\Rightarrow 2x-1=x+2$
$\Rightarrow x=3$
(0.5 Marks)

So, the first term of the AP is $a=x+1=3+1=4.$
The second term of the AP is $3x=3\times 3=9.$
$\therefore \text{Common difference,}d=9–4=5$
(0.5 Marks)

The $n^{\text{th}}$ term of an AP with first term $a$ and common difference $d$ is given by
$t_n=a+(n-1)d.$
$\Rightarrow t_5=4+4\left(5\right)=24$
(1 Mark)