Final answer:
The fifth term of the geometric sequence with a first term of 10 and a common ratio of 5 is found to be 6250 by using the geometric sequence formula, making the correct answer option (a).
Step-by-step explanation:
To find the fifth term of the geometric sequence with a first term of a = 10 and a common ratio of r = 5, you need to use the formula for the nth term of a geometric sequence, which is an = a * rn-1.
In this case, to find the 5th term (a5), you would plug in the values for a and r and the term number into the formula:
a5 = 10 * 55-1
a5 = 10 * 54 which equals 10 * 625.
Therefore, the fifth term of the geometric sequence is 6250, which corresponds to option (a) from the given choices.
To find the fifth term of a geometric sequence, we can use the formula:
Tn = a * r(n-1)
Where Tn is the nth term of the sequence, a is the first term, and r is the common ratio.
Plugging in the values, we get:
T5 = 10 * 5(5-1)
Simplifying, we have:
T5 = 10 * 54 = 10 * 625 = 6250