Question

Next term of the series will be 2,3,7,16,32​

Answer 1

Answer:

Step-by-step explanation:

If you look at the difference between numbers, you could observe a pattern,

3–2 = 1

7–3 = 4

16–7 =9

32–16 = 16

57–32 = 25

So the difference series is 1,4,9,16,25,……. which is the square of natural numbers

= 1^2,2^2,3^2,4^2,5^2,….

So the difference to the next number will be 6^2 = 36

So number is 57 + 36 = 93.

Answer is 93

Note : A generic equation for this series can be derived,

1st term = 2

2nd term = 2 + 1^2

3rd term = 2 + 1^2 + 2^2

:

nth term = 2 + 1^2 + 2^2 + 3^2 + … + (n-1)^2 ….

…… see equation for sum of squares for n terms

= 2 + (n(n-1)(2n-1) / 6)

For example , here 7th term has to found, there for

7th term = 2 + ((7*6*13)/6)

= 2 + (7*13) = 2 + 91 = 93 :)

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Sarvesh Shukla

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Minnu Sri

Minnu Sri, Owner at Techbuzzer.in (2018-present)

Answered Aug 13, 2018

Is justThe answer is 93

Here you can see how is it possible

The given question is

What is the next term to this series, 2, 3, 7, 16, 32, and 57?

As you can see the actual expansion

2 = 2

2+1*1 =3,

3+2*2 =7,

7+3*3 =16,

16+4*4 =32,

32+5*5 =57,

57+6*6=93.

The answer is 93

Answer 2

Answer:

57

Step-by-step explanation:

Tip

• The problems are based on a numerical pattern that is governed by a logical rule.

Find

next number of series

Solution

2,3=Gap 1=$1^{2}$

3,7=Gap 4=$2^{2}$

7,16=Gap 9=$3^{2}$

16,32=Gap 16=$4^{2}$

Next number should be gap of $5^{2} =25$

32,57

Final Answer

57

#SPJ2