Question

Is $302$ a term of the A.P. $3,8,13,.....$?

Answer 1

Ans.

given A.P is

$3,8,13,.....$

first term of this A.P is $a_1=3$

second term of this A.P is $a_2=8$

common difference of an A.P is given by

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

putting n=1 in above equation

$d=a_2-a_1=8-3=5$

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

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

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

$⟹a_n=3+(n-1)\left(5\right)$

$⟹a_n=3+5n-5$

$⟹a_n=-2+5n...eq\left(1\right)$

we have to find is $a_n=302$ is a term of this A.P

put $a_n=302$ in eq(1)

$⟹302=-2+5\times n$

$⟹5\times n=302+2$

$⟹n=\frac{304}{5}$

$⟹n=60.8$

but we know that n can't be an fractional number, it must be an integer(i.e., we can't have 60.8th term in our A.P)

$hence302isnotantermofthisA.P$