Question

Please use the information below for an arithmetic sequence to do the following:

a. sub 1 equals 3 d equals 4

A) List the first 6 terms of the sequence

B) Write the terms of this sequence as a series.

C) Provide a graph of the aritmetic sequence.

D) List the first 6 partial sums of the series.

SHOW ALL MATH WORK AND EXPLANATIONS FOR THIS FROM START TO FINISH! IT'S A 10 POINT PROBLEM!

Answer 1

See below, please.

Explanation:

A) The first term of the sequence is given as sub 1 = 3 and the common difference is given as d = 4. Therefore, the first 6 terms of the sequence are

sub 1 = 3

sub 2 = sub 1 + d = 3 + 4 = 7

sub 3 = sub 2 + d = 7 + 4 = 11

sub 4 = sub 3 + d = 11 + 4 = 15

sub 5 = sub 4 + d = 15 + 4 = 19

sub 6 = sub 5 + d = 19 + 4 = 23

B) The terms of this sequence can be written as a series as

3 + 7 + 11 + 15 + 19 + 23 + ...

C) The graph of the arithmetic sequence is a straight line with a positive slope, as each term of the sequence is obtained by adding a constant (d = 4) to the previous term.

D) The first 6 partial sums of the series can be calculated as

S1 = 3

S2 = 3 + 7 = 10

S3 = 3 + 7 + 11 = 21

S4 = 3 + 7 + 11 + 15 = 36

S5 = 3 + 7 + 11 + 15 + 19 = 55

S6 = 3 + 7 + 11 + 15 + 19 + 23 = 78

Therefore, the first 6 terms of the sequence are 3, 7, 11, 15, 19, and 23. The terms of the sequence can be written as a series as 3 + 7 + 11 + 15 + 19 + 23 + ..., and the graph of the sequence is a straight line with a positive slope. The first 6 partial sums of the series are 3, 10, 21, 36, 55, and 78.