Question

Use the sequence below to complete each task. 1, 5, 9, 13, ... a Identify the common difference (a). b. Write an equation to represent the sequence. C. Find the 7th term (a)

Answer 1

Given the sequence:

1, 5, 9, 13, ...........

a) To identify the common difference, use the formula:

d = a2 - a1

where, a2 = Second term

a1 = first term

Thus,

d = 5 - 1 = 4

Therefore, the common difference is 4

b) Write an equation to represent the sequence:

Use the arithmetic sequence formula:

`a_n\text{ = }a_1+(n\text{ - 1) d}`

where,

a1 = first term

n = number of terms

d = common diffrence

Thus the equation to represent the sequence is:

`a_7=1+(7-1)4`

c) To find the 7th term we have:

`\begin{gathered} a_7=1+(7-1)4 \\ \\ a_7\text{ = 1 + 24} \\ a_7\text{ = 25} \end{gathered}`

The 7th term is 25

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