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What is the fifth term of the geometric sequence a1=120, a2=36, a3=10.8, a6=0.2916?

What is the fifth term of the geometric sequence a1=120, a2=36, a3=10.8, a6=0.2916?
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Sarai Dooley Jr.

Feb 20, 2025

First we need to find the common ratio by dividing the second term by the first term. 36/120 = 3/10an = a1 * r^(n-1)n = term to find = 5a1 = first term = 120r = common ratio = 3/10now we sub and solvea5 = 120 * 3/10^(5 - 1)a5 = 120 * 3/10^4a5 = 120 * .0081a5 = 0.972 <=== fifth termor we could have just done thissince we multiply by 3/10 to find the next number...a3 = 10.810.8 * 3/10 = 3.24 <== 4th term3.24 * 3/10 = 0.972 <== fifth term... Show More
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S
Sarai Dooley Jr.

Feb 20, 2025

The formula for geometric sequence is an = a1 r^(n-1) where r is the geometric factor and n is an interger. In the sequence given, r is equal to 3/10. In this case, an = 120* (3/10)^(n-1). Solving for a5, a5 = 120* (3/10)^(5-1) = 0.972... Show More
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S
Sarai Dooley Jr.

Feb 20, 2025

Geometric Series PART 11. D2. D3. A4. C5. A6. D7. A8. A9. C10. A11. Chope this helps 🙂Step-by-step explanation: 100%... Show More
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S
Sarai Dooley Jr.

Feb 20, 2025

R = a2/a1 = 36/120 = 0.2a5 = a1 * r^4 = 120 * 0.2^4 = 120 * 0.0016 = 0.192Hope it helps!... Show More
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