Name the next number in the following sequence: 5, 9, 25, 89.....
Answers
Answer:
345
Step-by-step explanation:
5 + 4 = 9 ( 5 + 4^1)
9 + 16 = 25 (9 + 4^2)
25 + 64 = 89 ( 25+ 4^3)
now, add 4^4 to 89
89+4^4
= 89 + 256
= 345
345 is the next number in the series.
5, 9, 25, 89, 345
Step-by-step explanation:
Given:
5, 9, 25, 89.
To find:
The next number.
Solution:
This series is a numerical series in which the numbers are arranged orderly to form a sequence.
The pattern is (x₁,x₂,x₃,x₄,x₅) are the numbers in the series thus x₁, (x₁+4¹)⇒x₂, (x₂+4²)⇒x₃, (x₃+4³)⇒x₄, (x₄+4⁴)⇒x₅.
The pattern of this series is the numbers (x₁,x₂,x₃,x₄,x₅) added with the multiplies of (4¹,4²,4³,4⁴) orderly to make a sequence.
x₁=5
5 ⇒9
⇒5+4¹
⇒5+4
x₂⇒9
The second number 9 is attained by adding the first number 5 with 4. Therefore, we get 9 the second number x₂.
9⇒25
⇒4²+9
⇒16+9
x₃ ⇒25
The third number 25 is attained by adding the second number 9 with 4². Therefore, we get 25 the third number.
25⇒89
⇒4³+25
⇒64+25
x₄ ⇒89
The fourth number 89 is attained by adding the third number 25 with 4³. Therefore, we get 89 the fourth number.
89⇒345
⇒4⁴+89
⇒256+89
x₅⇒345
The fifth number 345 is attained by adding the fourth number 89 with 4⁴. Therefore, we get 345 the fifth number x₅.
The next number in the series is
89⇒ 345
Hence,
The next number in the series is 345.
5, 9, 25, 89, 345