Answer :
To find the 12th term of the geometric sequence 3, 15, 75,... use the formula aₙ = a ₁* [tex]r^{n-1}[/tex]With a= 3 and r = 5, the 12th term is 146484375.
The given sequence is 3, 15, 75,... To find the 12th term of the geometric sequence, we need to use the formula for the nth term of a geometric sequence:
aₙ= a₁ * [tex]r^{n-1}[/tex]
Where:
- a₁ is the first term of the sequence.
- r is the common ratio.
- n is the term number.
For the given sequence:
- a₁ = 3
- r (common ratio) can be found by dividing the second term by the first term:
r = 15 / 3 = 5
Now, we can find the 12th term (a₁₂):
a₁₂= 3 * [tex]5^{12-1}[/tex] = * [tex]5^{11}[/tex]
Calculating [tex]5^{11}[/tex] :
[tex]5^{11}[/tex] = 48828125
Therefore, the 12th term is:
a₁₂ = 3 * 48828125 = 146484375
So, the 12th term of the sequence is 146484375.
Answer:
146484375
Step-by-step explanation:
Use Formula: ar^n-1 = Term of the sequence (12th in this case)
a = first term (3)
r = multiplier (5)
n= number of terms (12)
3(5)^12-1 = 146484375
