Chapter 7.5, Problem 77MR

To determine

Todescribe:The pattern for given sequence and to write next three numbers in the sequence.

Answer to Problem 77MR

The pattern of the sequence $\langle s_n\rangle =1,4,9,\dots$ is $\langle s_n\rangle =1,4,9,16,25,36,\dots ,n^2,\dots$ , and next three terms of the sequence are $16,25,36$ .

Explanation of Solution

Given information:

The given sequence is $1,4,9,\dots$

Concept used:

A sequence is an arrangement of a list of numbers in a definite order. The numbers forming the sequence are known as its terms. The definite order or the pattern of the sequence

can be expressed by a formula involving natural number n .

Calculations:

The given sequence is $\langle s_n\rangle =1,4,9,\dots$ .

The terms of the sequence are squares of natural numbers.

Therefore, the sequence may be written as:

  $\langle s_n\rangle =1,4,9,16,25,36,\dots ,n^2,\dots$

Hence, next three terms of the sequence $\langle s_n\rangle =1,4,9,\dots$ are $16,25,36$ .

Conclusion:

The pattern of the sequence $\langle s_n\rangle =1,4,9,\dots$ is $\langle s_n\rangle =1,4,9,16,25,36,\dots ,n^2,\dots$ , and next three terms of the sequence are $16,25,36$ .