August 6, 2018

What is the 20th term of the arithmetic sequence 13, 19, 25, 31, ...?

The common difference is 19 – 13 = 6. Now that we know that we can find the 20th term by 13 + 6(20 – 1). Thus, the 20th term is 127.

What is the sum of A and B in the arithmetic sequence 7, 15, 23, A, 39, B, ...?

The common difference is 15 – 7 = 8. Therefore, A is 23 + 8 = 31 and B is 39 + 8 = 47. The sum A + B is 31 + 47 = 78.

What is the sum of A and B from the geometric sequence 32, A, 72, B, 162, 243...?

In a geometric sequence, any term after the first is equal to the geometric mean of the term immediately preceding it and the term immediately following it. This means that 32/A = A/72 → A2 = 2304 → A = 48. Additionally, 72/B = B/162 → B2 = 11,664 → B = 108. So, the sum A + B is 48 + 108 = 156.

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