Question

Let an denote the nth term of a geometric sequence. let a0=256 and an+1=0.5an .

Answer 1

The explicit formula is $a_{n-1} = 256 * 0.5^{n-1$ and the sum of the first 25 terms is approximately 512

The explicit formula

The given parameters are:

$a_0 = 256$

$a_{n +1} = 0.5a_n$

Set n = 0

$a_1 = 0.5a_0$

Substitute 256 for a0

$a_1 = 0.5 * 256$

$a_1 = 128$

This means that the common ratio is 0.5.

The explicit formula is then represented as:

$a_{n-1} = a_0 * r^{n-1$

This gives

$a_{n-1} = 256 * 0.5^{n-1$

The sum of the first 25 terms

This is calculated using:

$S_n = \frac{a_0(r^{n-1} -1)}{r - 1}$

This gives

$S_{25} = \frac{256 * (0.5^{25-1} -1)}{0.5 - 1}$

Evaluate

$S_{25} = 512$

Hence, the sum of the first 25 terms is approximately 512

Read more about geometric series at:

brainly.com/question/24643676

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