Asked by Jack_from_8th_grade
Given the following sequence, answer the questions below: 125, 100, 80, 64,.... (3 points) The starting value for the sequence is The common ratio is The fifth term is the sequence is
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Answered by
GPT-4o mini
To analyze the given sequence: 125, 100, 80, 64, we will determine the starting value, the common ratio, and the fifth term.
1. **Starting Value**: The starting value for the sequence is the first term, which is **125**.
2. **Common Ratio**: To find the common ratio, we will divide each term by the previous term:
- From 125 to 100:
\[ \frac{100}{125} = 0.8 \]
- From 100 to 80:
\[ \frac{80}{100} = 0.8 \]
- From 80 to 64:
\[ \frac{64}{80} = 0.8 \]
The common ratio is **0.8**.
3. **Fifth Term**: To find the fifth term, we can continue applying the common ratio to the last term we have (64):
- Fourth term (64) to fifth term:
\[ 64 \times 0.8 = 51.2 \]
Thus, the answers are:
- The starting value for the sequence is **125**.
- The common ratio is **0.8**.
- The fifth term in the sequence is **51.2**.
1. **Starting Value**: The starting value for the sequence is the first term, which is **125**.
2. **Common Ratio**: To find the common ratio, we will divide each term by the previous term:
- From 125 to 100:
\[ \frac{100}{125} = 0.8 \]
- From 100 to 80:
\[ \frac{80}{100} = 0.8 \]
- From 80 to 64:
\[ \frac{64}{80} = 0.8 \]
The common ratio is **0.8**.
3. **Fifth Term**: To find the fifth term, we can continue applying the common ratio to the last term we have (64):
- Fourth term (64) to fifth term:
\[ 64 \times 0.8 = 51.2 \]
Thus, the answers are:
- The starting value for the sequence is **125**.
- The common ratio is **0.8**.
- The fifth term in the sequence is **51.2**.
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