# which term of ap13 21 29 ........ will be 48 less than its 19 th term

Here , a = 13 , d = 21 - 13 = 8 , n = 19

We know that ,

a

_{n}= a + (n - 1)d

a

_{19}= 13 + ( 19 - 1)8

a

_{19}= 13 + (18) * 8 = 13 + 144 = 157

Thus, a

_{19}= 157

But , we have to find the term which is 48 less than the 19

^{th}term.

a

_{n}= a

_{19}- 48

a

_{n}= 157 - 48 = 109

Now , the term which is 48 less than 19th term is -:

a

_{n}= a + (n - 1)d

109 = 13 + (n - 1)8

96 = (n - 1)8

n - 1 = 96/8 = 12

n = 12 + 1 = 13

Hence , its 13th term will be 48 less than its 19th term.

**
**