Question

Which term of the a. P 3,8,13,18......... is 78?

Answer 1

Hi there!

a=3,d=8-3=5 and an=78

So, an=a +(n-1)d
78=3+(n-1)5
75=5n-5
5n=75+5
5n=80
n=16

Hence 78 is the 16th term of the AP.

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

★Here :-

a = 3

$\rightarrow{d=t_{2}-t_{1}}$

= 8 - 3

= 5

★Now we have :-

$\rightarrow{a_{n}=78}$

a + (n - 1)d = 78

${\boxed{\sf\:{Substitute\;the\;values\;we\;get}}}$

3 + (n - 1) × 5 = 78

(n - 1) × 5 = 78 - 3

(n - 1) × 5 = 75

${\boxed{\sf\:{(n-1)=\dfrac{75}{5}}}}$

(n - 1) = 15

n = 15 + 1

n = 16

$\fbox{Here we get that 78 is the 16th term of an AP}$