4, 25, 121, 289,529,?. What will be the next number in the series?
(a) 729
(b) 841
(c) 784
(d) 961
Answers
Answer:
here your answer.,.....
961
2*2=4
3
5*5=25
7
11*11=121
13
17*17=289
19
23*23=529
29
31*31=961
Given:
A series of numbers 4, 25, 121, 289, 529.
To Find:
The next term in the series.
Solution:
The given problem can be solved by developing a common logic between every term.
1. The first term in the series is obtained using the logic,
=> 4 = 2², ( 2 is a prime number).
2. The second term in the series is obtained using the logic,
=> 25 = 5², ( 5 is a prime number).
3. The third term in the series is obtained using the logic,
=> 121 = 11². ( 11 is a prime number).
4. The fourth term in the series is obtained using the logic,
=> 289 = 17².
5. The fifth term in the series is obtained using the logic,
=> 529 = 23².
6. The series can be also written as 2², 5², 11², 17², 23².
=> Squares of the alternate prime numbers denote the above series.
=> Next term = (2nd prime number after 23)^2,
=> Next term = 31²,
=> Next term = 961.
Therefore, the next term in the series is 961. Option D is the correct answer.