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Next number 2, 5, 11, 20, 32, 47?

Next number 2, 5, 11, 20, 32, 47?

Grade:12th pass

3 Answers

Vikas TU
14149 Points
9 years ago
Yeah absolutely keep adding the multiples of 3 in your given series. 
3+2=5 
6+5=11 
9+11=20 
12+20=23 
15+32=47 
18+47=65 
So the next number will 65.
Vikas TU
14149 Points
9 years ago
second method:
 
Series 2, 5, 11, 20, 32, 47 
Find = next number 
In this series each digit has the difference of 3,6,9,12,15 etc.. 
so next series will have the difference of 18. 
It means next number will be 47+18 = 65.
Vikas TU
14149 Points
9 years ago
3rd on1:
Solution: 

i) t₂ - t₁ = 5 - 2 = 3 
t₃ - t₂ = 6 
t₄ - t₃ = 9 and so on... 
So let the nth term - (n-1)th term be = x. 

ii) Sum of all the above = nth term - t₁ = 3 + 6 + 9 + ----- [This is in AP, whose first term = 3 and common difference = 3 and number of terms = (n - 1); the sum of which = [(n - 1)/2}*[2*3 - {(n - 1) - 1}*3] = 3n(n - 1)/2] 

Thus nth term - t₁ = 3n(n - 1)/2 
==> nth term = 3n(n - 1)/2 + 2 = (3n² - 3n + 4)/2 

As you require 7th term, n = 7 
Substituting the same in the above, 7th term = (3*7² - 3*7 + 4)/2 = 130/2 = 65
 

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