The nth term of a sequence where the difference between successive terms forms an arithmetic progression is typically given by a quadratic function. This is because the second difference (the difference of the differences) is constant in an arithmetic progression, which is a property of quadratic functions.

The general form of the nth term of such a sequence can be given by:

an^2 + bn + c

where:
- 'a' is half of the second difference (the constant difference between the differences of successive terms),
- 'b' is the difference between the first term and the sum of 'a' and 'c',
- 'c' is the first term in the sequence.

To find the values of 'a', 'b', and 'c', you would need specific information about the sequence, such as the first few terms or the common difference in the arithmetic progression of differences.

Question

The nth term of a sequence where the difference between successive terms forms an arithmetic progression is typically given by a quadratic function. This is because the second difference (the difference of the differences) is constant in an arithmetic progression, which is a property of quadratic functions.

The general form of the nth term of such a sequence can be given by:

an^2 + bn + c

where:
- 'a' is half of the second difference (the constant difference between the differences of successive terms),
- 'b' is the difference between the first term and the sum of 'a' and 'c',
- 'c' is the first term in the sequence.

To find the values of 'a', 'b', and 'c', you would need specific information about the sequence, such as the first few terms or the common difference in the arithmetic progression of differences.

Knowee AI · Accepted Answer

The nth term of a sequence where the difference between successive terms forms an arithmetic progression is typically given by a quadratic function. This is because the second difference (the difference of the differences) is constant in an arithmetic progression, which is a property of quadratic functions.

The general form of the nth term of such a sequence can be given by:

an^2 + bn + c

where:
- 'a' is half of the second difference (the constant difference between the differences of successive terms),
- 'b' is the difference between the first term and the sum of 'a' and 'c',
- 'c' is the first term in the sequence.

To find the values of 'a', 'b', and 'c', you would need specific information about the sequence, such as the first few terms or the common difference in the arithmetic progression of differences.

A sequence is such that, the difference between successive terms form an arithmetic progression, then its nth term is given by:

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