Find out series
3,10,32,100....?
Answers
3 * 3 + 1 = 10
3 * 10 + 2 = 32
3 * 32 + 4 = 100
3 * 100 + 8 = 308
306 is the next number in the series.
3,10,32,100, 306
Step-by-step explanation:
Given:
3,10,32,100.
To find:
The next number in the series.
Solution:
This series is a numerical sequence in which the numbers are arranged orderly and make a sequence.
The pattern is (x₁,x₂,x₃,x₄,x₅,x₆) are the numbers in the series thus x₁, (x₁×2)-5⇒x₂, (x₂×2)-4⇒x₃, (x₃×2)-3⇒x₄, (x₄×2)-2⇒x₅, (x₅×2)-1⇒x₆.
The pattern of this series is the multiplies of (3,3²,3³,3⁴,3⁵) get added with (1, (1×3)+2, (5×3)+4, (19×3)+6) numbers. Thus we get the series.
First number x₁=3
3 ⇒10
⇒3²+1
⇒9+1
x₂⇒10
The second number 10 is obtained by 3² gets added with 1. Thus we get 10, the second number x₂.
10⇒32
⇒3³+(1×3)+2
⇒27+5
x₃⇒32
The third number 32 is obtained by adding 3³ with the previous 1 multiplied by 3 and gets added with 2 . Thus we get 32, the third number x₃.
32⇒100
⇒3⁴+(5×3)+4
⇒81+15+4
⇒81+19
x₄⇒100
The fourth number 100 is obtained by adding 3⁴ with the previous 5 multiplied by 3 and gets added with 4. Thus, we get 100, the fourth number x₄.
100⇒306
⇒3⁵+(19×3)+6
⇒243+57+6
⇒243+63
x₅⇒306
The fifth number 306 is obtained by adding 3⁵ with the previous 19 multiplied by 3 and gets added with 6. Thus we get 306, the fifth number x₅.
The next number in the series is
100⇒ 306
Hence,
The next number in the series is 306.
3,10,32,100, 306