Question

Find any of the values a_1, r, a_n, n, or S_n that are missing from the geometric sequence.

r=5/3, n=4, S_4=816
The value of a_1 is__

Answer 1

The value of a_1 in the given geometric sequence is 176.064.

Step-by-step explanation:

In a geometric sequence, each term is found by multiplying the previous term by a constant called the common ratio (r). To find the value of a1, we can use the formula:

an = a1 * r(n-1)

Since we know the value of r and n, we can rearrange the formula to solve for a1:

a1 = an / r(n-1)

Plugging in the given values, we have: a1 = 816 / (5/3)(4-1)

Simplifying, we get a1 = 816 / (125/27) = 816 * 27 / 125 = 176.064

Therefore, the value of a1 is 176.064.