Chapter 7.5, Problem 72MR

To determine

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

Answer to Problem 72MR

The pattern of given sequence is $3,6,9,\dots ,3n,\dots$ , where $n=1,2,3,\dots$ , and next three terms of sequence are 12, 15, and 18.

Explanation of Solution

Given information:

The given sequence is $3,6,9,\dots$

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 $\langle s_n\rangle =3,6,9,\dots$ .

The terms of the sequence are the multiple of 3. Therefore, the sequence may be written as

  $\langle s_n\rangle =3\times 1,3\times 2,3\times 3,\dots ,3\times n,\dots$

Thus, the formula or the pattern of the sequence $\langle s_n\rangle$ is $s_n=3n$ , where $n=1,2,3,\dots$ .

From the formula, $s_n=3n$ the sequence may be written as:

  $\langle s_n\rangle =3,6,9,\underset{\_}{12,15,18},21,\dots$

Hence, next three terms of the sequence $\langle s_n\rangle =3,6,9,\dots$ are 12, 15, and 18.

Conclusion:

The pattern of given sequence $\langle s_n\rangle =3,6,9,\dots$ is $s_n=3n$ , where $n=1,2,3,\dots$ , and next three terms of the sequence are 12, 15, and 18.