APPC SOS #5 Days 1-4 Practice

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. For example, in the sequence 2, 5, 8, 11, the common difference is 3.

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How do you find the nth term of an arithmetic sequence?

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The nth term of an arithmetic sequence can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term, d is the common difference, and n is the term number.

Front

What is a geometric sequence?

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A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. For example, in the sequence 3, 6, 12, 24, the common ratio is 2.

Front

How do you find the nth term of a geometric sequence?

Back

The nth term of a geometric sequence can be found using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and n is the term number.

Front

What is the formula for the sum of the first n terms of an arithmetic sequence?

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The formula for the sum of the first n terms (S_n) of an arithmetic sequence is: S_n = n/2 * (a_1 + a_n), where a_1 is the first term and a_n is the nth term.

Front

What is the formula for the sum of the first n terms of a geometric sequence?

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The formula for the sum of the first n terms (S_n) of a geometric sequence is: S_n = a_1 * (1 - r^n) / (1 - r), where a_1 is the first term and r is the common ratio.

Front

Find the 32nd term of the sequence: 9, 4, -1, -6, -11, ...

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The 32nd term is -146.

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Find the 22nd term of the sequence: 5, 8, 11, ...

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The 22nd term is 68.

Front

What is the next term in the series: 4, 16, 64?

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The next term is 256.

Front

Is the sequence 6, 18, 54 arithmetic or geometric?

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The sequence is geometric.