Question

Find the explicit formula for the geometric sequence bn with the following information given.

b1=7
b4=−56/27

Answer 1

The explicit formula for the geometric sequence bn is bn = 7 * (-2/3)^(n-1), where r = -2/3 is the common ratio determined from the given terms.

Step-by-step explanation:

To find the explicit formula for the geometric sequence, we need to determine the common ratio (r) first. We can do this by dividing any term in the sequence by its previous term.

Using the given information, we have:

b4 = b1 * r3

Substituting the values, we get:

-56/27 = 7 * r3

Now, solve for r:

r3 = (-56/27) / 7

r3 = -8/27

Taking the cube root of both sides, we find:

r = -2/3

Now that we know the common ratio, we can write the explicit formula:

bn = b1 * r(n-1)

Substituting the values, we have:

bn = 7 * (-2/3)(n-1)