A series is given with one term missing. Select the correct alternative from the given ones that will complete the series.
4, 9, 25, 64, 169, ?
- A441
- B225
- C289
- D256
Solution & Step-by-step Explanation
Let's evaluate the given terms as perfect squares:
4=2
2
9=3
2
25=5
2
64=8
2
169=13
2
Notice the base numbers under the squares: 2,3,5,8,13.
This forms a Fibonacci-like sequence where each subsequent base is the sum of the previous two bases:
2+3=5
3+5=8
5+8=13
8+13=21
So, the next base number is 21.
The next term in the series will be 21
2
=441.
4=2
2
9=3
2
25=5
2
64=8
2
169=13
2
Notice the base numbers under the squares: 2,3,5,8,13.
This forms a Fibonacci-like sequence where each subsequent base is the sum of the previous two bases:
2+3=5
3+5=8
5+8=13
8+13=21
So, the next base number is 21.
The next term in the series will be 21
2
=441.