Question

write the next two numbers 13 39 65 ___ ___

Answer 1

91,117 .
Because they are in AP and their common difference is 26

Answer 2

Given,

The first, second and third terms are 13 39 65 respectively

To Find,

The fourth and fifth terms of a given sequence

Solution,

First of all, we will check whether the given sequence is A.P. or not.

For that, we will compare the difference between consecutive terms ie

Difference between first and second term = 39 - 13 = 26

Difference between second and third  term = 65- 39 = 26

The difference between consecutive terms is the same so it is an A.P.

By formula, $a_{n}=a_{1}+(n-1)d$ we can find the 4th and 5th terms of A.P.

$a_{4}=a_{1}+(n-1)d$ (Where a = 13 ,d  = 26  and n =4 )

$a_{4}= 13 +( 4-1)*26$

$a_{4}=13 +3* 26 \\ a_{4} = 13+78\\ a_{4} = 91$

Similar;y for the 5th term,

$a_{5}=a_{1}+(5-1)d$

$a_{5}= 13 +(4)*26\\a_{5} = 13 + 104\\a_{5} = 117$

Hence, the next two numbers of the given sequence are 91 and 117