Answer:
Explanation:
Let me explain step by step:
Determine the common ratio: We see that each term is half the previous term, so the common ratio is 1/2.
Write the formula for the nth term: We can use the formula for an infinite geometric series to find the nth term:
a_n = a_1 * r^(n-1), where a_1 is the first term (60), r is the common ratio (1/2), and n is the term number.
Plug in the values: We want to find the 9th term, so we plug in the values into the formula:
a_9 = 60 * (1/2)^(9-1)
Calculate the expression: We can simplify the expression by using the exponent rule for powers of 1/2:
a_9 = 60 * (1/2)^8
Divide the result by 256: We can simplify the expression further by dividing both sides by 256:
a_9 = 60 * 1/256
a_9 = 60 / 256
Get the final answer: We divide 60 by 256 to get the final answer:
a_9 = 0.234375
So the 9th term of the sequence is approximately 0.234375.