Question

Find the general term of the following sequence
1.5. 14.30,55​

Answer 1

Answer:

Step-by-step explanation:

Very tough question

Answer 2

Answer:

The second term, 14, is 9 more than the previous term, 5.

The third term, 30, is 16 more than the previous term, 14.

The fourth term, 55, is 25 more than the previous term, 30.

The fifth term, 91, is 36 more than the previous term, 55.

Now, lets look at the values by which each succesive term is increasing.

First increment is 9, which is the square of 3.

Second increment is 16, which is the square of 4.

Third increment is 25, which is the square of 5.

Fourth increment is 36, which is the square of 6.

Therefore, each increment is a square of a natural number, starting with 3, in proper increasing order.

The next natural number after 6 is 7. Therefore, the next increment should be the square of 7, which is 49.

Last given term is 91. Adding 49 to 91, we get 140.

Therefore, the next number in the sequence is 140.