Question

If numbers $n-2,4n-1$ and $5n+2$ are in A.P., find the value of $n$ and its next two terms.

• A. $n=0$ and next two terms are $3,5$
• B. $n=1$ and next two terms are $11,15$
• C. $n=2$ and next two terms are $17,22$
• D. $n=-1$ and next two terms are $-4,-5$

Answer 1

The correct option is B $n=1$ and next two terms are $11,15$

$n-2,4n-1,5n+2$ are in A.P.

First term, $a_1=n-2$

Second term, $a_2=4n-1$

Third term, $a_3=5n+2$

Common difference (difference of two consecutive terms),

$d=a_2-a_1=a_3-a_2$

$4n-1-(n-2)=5n+2-(4n-1)$

$4n-1-n+2=5n+2-4n+1$

$3n+1=n+3$

$2n=2$

$n=1$

So,

$a_1=n-2=1-2=-1$

$a_2=4n-1=4-1=3$

and $d=a_2-a_1=3-(-1)=4$

$nth$ term of an AP is ,

$a_n=a+(n-1)d$

where,

$a=$first term

$d=$common difference

Therefore,

$a_4=a+3d=-1+12=11$

$a_5=a+4d=-1+16=15$