Chapter 7.5, Problem 75MR

To determine

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

Answer to Problem 75MR

The pattern of the sequence $\langle s_n\rangle =2,7,12,\dots$ is $s_{n+1}=s_n+5$ , $s_1=2$ , and $n=1,2,3,\dots$ .., and next three terms of the sequence are $17,22,27$ .

Explanation of Solution

Given information:

The given sequence is $2,7,12,\dots$

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 $\langle s_n\rangle =2,7,12,\dots$ .

The consecutive terms of the sequence are such that a term is 5 greater than preceding term. Therefore, the sequence $\langle s_n\rangle$ may be written as

  $\langle s_n\rangle =2,7,12,\dots ,s_n,s_{n+1}=s_n+5,\dots$ , where $n=1,2,3,\dots$

Thus, the formula or the pattern of the sequence $\langle s_n\rangle$ is $s_{n+1}=s_n+5$ , and $s_1=2$ .

From the formula, $s_{n+1}=s_n+5$ , $s_1=2$ , and $n=1,2,3,\dots$ . the sequence may be written as:

  $\langle s_n\rangle =2,7,12,\underset{\_}{17,22,27,}\dots$

Hence, next three terms of the sequence $\langle s_n\rangle =2,7,12,\dots$ are $17,22,27$ .

Conclusion:

The pattern of the sequence $\langle s_n\rangle =2,7,12,\dots$ is $s_{n+1}=s_n+5$ , $s_1=2$ , and $n=1,2,3,\dots$ .., and next three terms of the sequence are $17,22,27$ .