Question

Which term of the A.P. $4,9,14,.....$ is $254$?

Answer 1

Given A.P is $4,9,14,,.....$

first term of this A.P is $a_1=4$

second term of this A.P is $a_2=9$

common difference of an A.P is given by

$(i.e.,d=a_{n+1}-a_n)$

putting n=1 in above equation

$d=a_2-a_1=9-4=5$

hence common difference for this A.P is $d=5$

the nth term of an A.P is given by.

$a_n=a_1+(n-1)d$

$⟹a_n=4+(n-1)\left(5\right)$

$⟹a_n=4+5n-5$

$⟹a_n=-1+5n...eq\left(1\right)$

we have to find which term$\left(n\right)$ of this A.P is $a_n=254$

put $a_n=254$ in eq(1)

$⟹254=-1+5\times n$

$⟹5\times n=254+1$

$⟹5\times n=255$

$⟹n=\frac{255}{5}$

$⟹n=51$

hence $51$th term of this A.P is $254$