Question

Find a₇ of the geometric sequence where a₁ is 11 and the common ratio is 5.

Answer 1

a₇ = 171875

Explanation:

The nth term of any geometric sequence is given by the formula:

`a_n = a_1 \cdot q^(n - 1)`

In our case, we're given that a₁ = 11, and q = 5, therefore:

`a_n = 11 \cdot 5^(n - 1)`

To find a₇, we'll substitute n = 7 into the sequence's formula:

`a_7 = 11 \cdot 5^(7 - 1)\\\to a_7 = 11 \cdot 5^6\\\to a_7 = 11 \cdot 15625\\\to a_7 = 171875`