Question

For a given geometric sequence, the 1ˢᵗ term, a₁, is equal to (43)/(25), and the 4ᵗʰ term, a₄, is equal to 215 . Find the value of the 8ᵗʰ term, a₈. If applicable, write your answ

Answer 1

To find the 8th term in a geometric sequence, divide the 4th term by the 1st term to find the common ratio. Then use the formula aₙ = a₁ * r^(n-1), where n is the term number, to find the 8th term.

Step-by-step explanation:

To find the value of the 8th term, a₈, in a geometric sequence, we need to find the common ratio, r. The common ratio can be found by dividing the 4th term, a₄, by the 1st term, a₁. In this case, a₄ = 215 and a₁ = 43/25.

r = a₄/a₁ = 215 / (43/25) = 215 * (25/43) = 125

Once we have the common ratio, we can find the 8th term using the formula aₙ = a₁ * r^(n-1), where n is the term number.

a₈ = (43/25) * 125^(8-1) = (43/25) * 125^7 = 50328125/25 = 2013125