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Questions and Answers
In a geometric series, what is the common ratio if the 4th term is 81 and the 7th term is 729?
What is the formula to find the nth term of an arithmetic sequence?
What is the sum of the first 15 terms of the arithmetic series 3, 7, 11, ... if the common difference is 4?
Study Notes
Geometric Series
- To find the common ratio of a geometric series, we can use the given terms: 4th term = 81 and 7th term = 729.
Arithmetic Sequence
- The formula to find the nth term of an arithmetic sequence is: an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.
Arithmetic Series
- To find the sum of the first 15 terms of an arithmetic series, we can use the formula: Sn = n/2 (a1 + an), where Sn is the sum of n terms, a1 is the first term, and an is the nth term.
- In this case, the common difference is 4, and we need to find the 15th term (an) to calculate the sum.
- Given the series 3, 7, 11, ..., the first term (a1) is 3, and we can use the formula an = a1 + (n - 1)d to find the 15th term.
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Description
Test your knowledge of sequences and series with this quiz for class 11. Explore the formulas for finding the nth term of an arithmetic sequence and the common ratio of a geometric series. Calculate the sum of the first 15 terms of an arithmetic series with a given common difference.
