Question

If the 1st and 10th terms of a geometric sequence are 3 and 30, respectively, find the 40th term (to three decimal places) of the sequence.

Posting this again because the last response said that
r⁹ = 10 becomes r=10¹/⁹

Answer 1

To find the 40th term of the geometric sequence, we can use the formula an = a1 * r(n-1). By substituting the given values of the first term and the tenth term, we can find the common ratio. Then, we can substitute the common ratio back into the formula to find the 40th term.

Step-by-step explanation:

To find the 40th term of a geometric sequence, we can use the formula:

an = a1 * r(n-1)

where an is the nth term, a1 is the first term, and r is the common ratio.

In this sequence, the first term (a1) is 3 and the tenth term (a10) is 30. We need to find the 40th term (a40).

Substituting the values into the formula:

a40 = 3 * r(40-1)

30 = 3 * r9

Divide both sides by 3:

10 = r9

To solve for r, we can take the ninth root of 10 (r9 = 10). Using a calculator:

r = 10(1/9)

Now we can substitute the value of r back into the formula to find the 40th term:

a40 = 3 * (10(1/9))(40-1)

Using a calculator to get an approximate value:

a40 ≈ 129.460