Question

1, 8, 9, 64, 25, ______​

Answer 1

Answer:

216

Step-by-step explanation:

the logic is

1 square =1

2cube = 8

3sqaure = 9

4cube = 64

5square = 25

so

6cube =216

Answer 2

Final answer: 1, 8, 9, 64, 25, 216    

Given that: We are given 1, 8, 9, 64, 25, ______​

To find: We have to find next term 1, 8, 9, 64, 25​

Explanation:

• Given logical sequence is 1, 8, 9, 64, 25, ______

• First we have to find the general formula of the given logical sequence.

             $1 = 1^{2} \\\\8=2^{3} \\\\9=3^{2}\\ \\64=4^{3}\\ \\25=5^{2}$

• In the above values, even values are the cubes of their respective term numbers.

i.e. for terms 2, 4 their corresponding values are 8 and 64

• The odd values in the sequences are squares of their respective term numbers.

i.e. for terms 1, 3, 5  their corresponding values are 1, 9 and 25

• Since the missing term is at position ‘6′ and it is even term no.

Missing term would be 6³ = 216

• The general formula of the logical sequence: let  ’x’ be the term number.

If ’x’ is even it is x³.

If ’x’ is odd, it is x².

• So, the sequence would be,

1, 8, 9, 64, 49, 216,……..,(2x)³, (2x + 1)²

• Hence, 1, 8, 9, 64, 25, 216    

To know more about the concept please go through the links

https://brainly.in/question/54184668

https://brainly.in/question/34337375

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