Question

which term of an A.P. 3,8,13,18,.............is 78?

Answer 1

a=3           d= 8-3 = 5              n=? 
$a_{n}$ = a+ (n-1)d
⇒78 = 3 + (n-1)5
⇒75 = (n-1)5
⇒n-1 = 15
⇒n = 16

∴78 is the 16th term of the given A.P.

Answer 2

For the following A.P : 3,8,13,18,------, 78 

First term (t1) = a = 3,common difference (d) = 8 - 3 = 5 and last term (tn) = 78 

The general term of A.P is 

tn = a + (n - 1) d 

78 = 3 + (n - 1)5 

78 = 3 + 5n - 5 

78 = - 2 + 5n 

78 + 2 = 5n 

80 = 5n 

80/5 = n 

16 = n 

n= 16 

16th term of A.P : 3,8,13,18,is 78.