Question

find the number

1,6,13,24,41,?​

Answer 1

Answer:

the next number is 62 it is the answer

Answer 2

68 is the missing number in the series.

1,6,13,24,41, 68

Step-by-step explanation:

Given:

1,6,13,24,41,?​

To find:

The missing number

Solution:

• This is a numerical sequence by which numbers are arranged in an orderly to form a series.
• The pattern in the series is (1², 2²+2, 3²+4, 4²+8, 5²+16, 6²+32)
• The pattern states that (1²,2²,3²,4²,5²,6²) all are natural number squares which are added with the (0,2,4,8,16,32) which is (2¹,2²,2³,2⁴,2⁵)a multiple of 2 terms that is (2, 2×2, 2×2×2,c2×2×2×2, 2×2×2×2×2)

The first number is 1²=1+0=1

The second number 6 is obtained by 2²+2 thus next natural number square with 2¹ we get,

1⇒6

⇒2²+2

⇒4+2=6

The third number 13 is obtained by 3²+4 thus next natural number square with 2² we get,

6⇒13

 ⇒ 3²+4

 ⇒9+4=13

The fourth number 24 is obtained by 4²+8 thus next natural number square with 2³ we get,

13⇒24

  ⇒4²+8

  ⇒16+8=24

The fifth number 41 is obtained by 5²+16 thus next natural number square with 2⁴ we get,

24⇒41

   ⇒5²+16

   ⇒25+16=41

The sixth number 68 is obtained by 6²+32 thus next natural number square with 2⁵ we get,

41⇒?

  ⇒6²+32

   ⇒36+32=68

Hence,

68 is the missing number in the series.

1,6,13,24,41, 68