Question

NO LINKS!!

Finish the table below:

n t(n)
1 7.5
2 3.75
3 1.875
4
5


b. Name the type of sequence

c. Find an equation for the sequence

Answer 1

a) See below.

b) Geometric sequence

`\textsf{c)} \quad a_n=7.5(0.5)^(n-1)`

Explanation:

Part (a)

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

Therefore:

`\implies a_4=1.875 / 2 = 0.9375`

`\implies a_5=0.9375 / 2 =0.46875`

Completed table:

`\begin{array}c\cline{1-2} \vphantom{\frac12} n&t(n) \\\cline{1-2} \vphantom{\frac12} 1& 7.5\\\cline{1-2} \vphantom{\frac12} 2& 3.75\\\cline{1-2} \vphantom{\frac12} 3&1.875 \\\cline{1-2} \vphantom{\frac12} 4& 0.9375\\\cline{1-2} \vphantom{\frac12} 5& 0.46875\\\cline{1-2} \end{array}`

Part (b)

As the given sequence has a constant ratio of 0.5, it is a geometric sequence.

Part (c)

`\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^(n-1)$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}`

The first term of the sequence is 7.5. Therefore,:

• a = 7.5

The common ratio is 0.5. Therefore:

• r = 0.5

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

• 
  `a_n=7.5(0.5)^(n-1)`