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

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.