Question

NO LINKS!!

Finish the table below:

n t(n)
4 33
5 43
6 53
7
8

b. Name the type of sequence

c. Find an equation for the sequence

Answer 1

a) See below.

b) Arithmetic sequence

`\textsf{c)} \quad a_n=10n-7`

Explanation:

Part (a)

From inspection of the given table, t(n) increases by 10 each time n increases by 1.

Therefore:

`\implies a_7=53+10=63`

`\implies a_8=63+10=73`

Completed table:

`\begin{array}\cline{1-2} \vphantom{\frac12} n&t(n) \\\cline{1-2} \vphantom{\frac12} 4& 33\\\cline{1-2} \vphantom{\frac12} 5& 43\\\cline{1-2} \vphantom{\frac12} 6&53 \\\cline{1-2} \vphantom{\frac12} 7&63\\\cline{1-2} \vphantom{\frac12} 8& 73\\\cline{1-2} \end{array}`

Part (b)

As the given sequence has a constant difference of 10, it is an arithmetic sequence.

Part (c)

`\boxed{\begin{minipage}{8 cm}\underline{General form of an arithmetic sequence}\\\\$a_n=a+(n-1)d$\\\\where:\\\phantom{ww}$\bullet$ $a_n$ is the nth term. \\ \phantom{ww}$\bullet$ $a$ is the first term.\\\phantom{ww}$\bullet$ $d$ is the common difference between terms.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}`

The common difference is 10. Therefore:

• d = 10

To find the first term, a, substitute the value of d and one of the terms into the formula:

`\begin{aligned}\implies a_4=a+(4-1)(10)&=33\\a+3(10)&=33\\a+30&=33\\&a=3\end{aligned}`

Therefore, to write an equation for the given arithmetic sequence, substitute the found values of a and d into the formula:

`\implies a_n=3+(n-1)(10)`

`\implies a_n=3+10n-10`

`\implies a_n=10n-7`