Practice Practice Problems (5) - Finite Series - IB 10 Mathematics

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6 sample questions

Question 1.
Find the sum of the first 5 terms of the series: 1 + 2 + 3 + 4 + 5.
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Use the formula for the sum of an arithmetic series.
Question 2.
Determine the common difference for the series: 7, 10, 13, 16.
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Subtract subsequent terms.
3Question 3.
What is the formula for the sum of the first n terms of an arithmetic series?
- S_n = n/2 * (2a + (n-1)d)
- S_n = a * r^n / (1 - r)
- S_n = n * (a + l)
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Think about the relationship between terms.
4Question 4.
If the common ratio r of a geometric series is equal to 1, what happens?
- True
- False
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Consider what a constant series means.
Question 5.
Prove that the sum of the first n terms of an arithmetic sequence can be expressed in multiple forms and solve for n = 50, a = 5, d = 3.
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Use the various formulas you've learned.
Question 6.
Consider a geometric series where a = 4 and r = 0.5. Determine the sum of the first 10 terms and its significance.
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Pay attention to the decimal behavior and convergence.

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