Answer :
Use the formula a(n) = a(1)*r^(n-1), where r is the common factor and n is the counter.
The first term, a(1), of 0.2, 1, 5, 25, 125, ... is obviously 0.2. Note that multiplying 0.2 by 5 gives us 1; mult. 5 by 5 gives us 25, etc., so the common factor r is 5.
Thus, a(n) = a(1)*r^(n-1) becomes a(n) = 0.2*(5)^(n-1), and
a(10) = 0.2*(5)^(10-1), or 0.2*5^9, or 0.2(1953125), or 390625 (answer)
The first term, a(1), of 0.2, 1, 5, 25, 125, ... is obviously 0.2. Note that multiplying 0.2 by 5 gives us 1; mult. 5 by 5 gives us 25, etc., so the common factor r is 5.
Thus, a(n) = a(1)*r^(n-1) becomes a(n) = 0.2*(5)^(n-1), and
a(10) = 0.2*(5)^(10-1), or 0.2*5^9, or 0.2(1953125), or 390625 (answer)
The 10th term in the given geometric sequence is 390,625. So, option h is correct.
What is the general form of a geometric sequence?
The general form or the nth term of a geometric sequence is [tex]a_n=a_1*r^(^n^-^1^)[/tex]. Where a1 is the first term in the sequence, r is the common ratio and n is the number of the term which is to be calculated.
The common ratio is calculated by the ratio of a data term to the previous term. I.e., [tex]r = \frac{a_n_+_1}{a_n}[/tex] or [tex]r=\frac{a_n}{a_n_-_1}[/tex].
Calculating the 10th term of the given geometric sequence:
The given geometric sequence is 0.2, 1, 5, 25, 125, ...
Step 1: finding the common ratio:
r = [tex]\frac{25}{5}[/tex]
= 5
Step 2: Finding the 10th term:
Where n = 10, r = 5 and a1 = 0.2
Sunstituting these values in the general form/term
[tex]a_1_0=0.2*(5)^(^1^0^-^1^)[/tex]
= [tex]0.2*5^9[/tex]
= 390,625
Therefore, the 10th term is 390,625 which is given at option h.
Learn more about geometric progression here:
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