Question

Write an explicit formula for the following sequence. Then generate the first five terms.

Answer 1

ANSWERS

• Explicit formula:

`a_n=768(0.25)^(n-1)`

• First 5 terms: ,768, 192, 48, 12, 3

Step-by-step explanation

The first term is 768 and the common ratio is 0.25. If this is a geometric sequence we have the form,

`a_n=a_1\cdot r^(n-1)`

Replace the first term and the common ratio,

`a_n=768(0.25)^(n-1)`

To find the first 5 terms we have to find an for n = 1, n = 2, n = 3, n = 4 and n = 5,

`a_1=768(0.25)^(1-1)=768(0.25)^0=768\cdot1=768`

The second term is,

`a_2=768(0.25)^(2-1)=768(0.25)^1=768\cdot0.25=192`

The third term,

`a_3=768(0.25)^(3-1)=768(0.25)^2=768\cdot0.0625=48`

The fourth term,

`a_4=768(0.25)^(4-1)=768(0.25)^3=768\cdot0.015625=12`

And the fifth term,

`a_5=768(0.25)^(5-1)=768(0.25)^4=768\cdot0.00390625=3`

Hence, the first five terms are 768, 192, 48, 12, 3.