Question

Determine the next three terms in the following sequence: 1, 8, 27, 64,____, ____, ____,...

a. 91, 155, 246
b. 87, 124, 247
c. 97, 142, 253
d. 125, 216, 343

Answer 1

Hello,

Answer D

`x_(n) =n^3\\ x_(1) =1^3=1\\ x_(2) =2^3=8\\ x_(3) =3^3=27\\ x_(4) =4^3=64\\ x_(5) =5^3=125\\ x_(6) =6^3=216\\ x_(7) =7^3=343\\`

Answer 2

d. 125, 216, 343

Explanation:

The given sequence is 1, 8, 27, 64,.......

Now, we can write

`1=1^3\\\\8=2^3\\\\27=3^3\\\\64=4^3`

Here, we can see that the first term is cube of 1, second term is cube of 2, third term is cube of 3 and so on.

Therefore, in order to find the 5th, 6th and 7th term of the sequence, we have to take cube of 5, 6 and 7 respectively.

Therefore, the next three terms of the sequence are

`5^3=125\\\\6^3=216\\\\7^3=729`

The correct option is d which is 125, 216, 343