Calculate a_5 for the geometric sequence in which a_1=1,600 and the common ratio is 3/4

Answer 1

To find the 5th term (a_5) of a geometric sequence, we can use the formula:

a_n = a_1 * r^(n-1)

Where a_1 is the first term, r is the common ratio, and n is the term number.

Given: a_1 = 1,600 and r = 3/4

Substituting the given values into the formula, we have:

a_5 = 1,600 * (3/4)^(5-1)

a_5 = 1,600 * (3/4)^4

Now, we can simplify the fraction (3/4)^4:

(3/4)^4 = (81/256)

Substituting back into the formula, we have:

a_5 = 1,600 * (81/256)

Next, we can calculate the value of a_5:

a_5 = 1,600 * 81/256

a_5 = 51,600/256

Finally, we can simplify the fraction:

a_5 = 201.5625

Therefore, the 5th term (a_5) of the given geometric sequence is approximately 201.5625.