Question

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

Answer 1

Answer:

d. 125, 216, 343

Step-by-step 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

Answer 2

Hello,

Answer D
$x_{n} =n^3\\ x_{1} =1^3=1\\ x_{2} =2^3=8\\ x_{3} =3^3=27\\ x_{4} =4^3=64\\ x_{5} =5^3=125\\ x_{6} =6^3=216\\ x_{7} =7^3=343$