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The first three terms of a sequence are given. Round to the nearest thousandth (if

necessary).
8, 40, 200, ...
Find the 10th term.

User Safiyah
by
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1 Answer

3 votes

Answer: Here you go

Explanation:

We can see that each term in the sequence is obtained by multiplying the previous term by 5. Therefore, the nth term can be found using the formula:

a_n = a_{n-1} * 5

where a_1 = 8.

Using this formula, we can find the 4th term:

a_2 = a_1 * 5 = 8 * 5 = 40

a_3 = a_2 * 5 = 40 * 5 = 200

a_4 = a_3 * 5 = 200 * 5 = 1000

So, the 10th term can be found as:

a_10 = a_9 * 5 = (a_8 * 5) * 5 = ((a_7 * 5) * 5) * 5 = ... = a_1 * 5^9

We can simplify this expression by noticing that 5^9 = 1953125. Therefore:

a_10 = 8 * 1953125 = 15625000

Rounding to the nearest thousandth gives us:

a_10 ≈ 15625.000

Therefore, the 10th term of the sequence is approximately 15625.000.