Question

find the next term in that sereis 9,49,121,225,361,------?

Answer 1

your ans

answer:- 529

explanation

9=(3)2

49=(7)2

121=(11)2

225=(15)2

361=(19)2

as they are increasing by 4

so

19+4=23

so

(23)2=529

Answer 2

Given: A series - 9,49,121,225,361,___

To find: the 6th term of this series.

Method of solving: the pattern of the series is $(3+4n)^{2}$.

Step-by-step explanation:

Step 1 of 2

The terms can be written as:

$9=3^{2}\\ \\49=7^{2} =(3+4)^{2} =(3+(4*1))^{2} \\\\121=11^{2} =(3+8)^{2} =(3+(4*2))^{2}\\ \\225=15^{2} =(3+12)^{2} =(3+(4*3))^{2} \\\\361=19^{2} =(3+16)^{2} =(3+(4*4))^{2}$

So, the pattern is $(3+4n)^{2},n=0,1,2,...$

Step 2 of 2

For the 6th term, n=5

So, it will be: $(3+(4*5))^{2}=(3+20)^{2} =23^{2} =529$

The next term in the series is 529.