Question

State the difference between Arithmetic Progression (A.P.) and Geometric Progression (A.P.).​

Answer 1

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Arithmetic Sequence

➻ Arithmetic Sequence is described as a list of numbers, in which each new term differs from a preceding term by a constant quantity.

➻ To put simply, in an arithmetic progression, we add or subtract a fixed, non-zero number, each time infinitely. If a is the first member of the sequence, then it can be written as:

a, a+d, a+2d, a+3d, a+4d..

where, a = the first term

d = common difference between terms

Example: 1, 3, 5, 7, 9..

5, 8, 11, 14, 17..

Geometric Sequence

➻Geometric Sequence is a set of numbers wherein each element after the first is obtained by multiplying the preceding number by a constant factor.

➻ In finer terms, the sequence in which we multiply or divide a fixed, non-zero number, each time infinitely, then the progression is said to be geometric. Further, if a is the first element of the sequence, then it can be expressed as:

a, ar, ar2, ar3, ar 4 ..

where, a = first term

d = common difference between terms

Example: 3, 9, 27, 81..

4, 16, 64, 256..

Differences Between Arithmetic and Geometric Sequence

• The following points are noteworthy so far as the difference between arithmetic and geometric sequence is concerned:

• As a list of numbers, in which each new term differs from a preceding term by a constant quantity, is Arithmetic Sequence. A set of numbers wherein each element after the first is obtained by multiplying the preceding number by a constant factor, is known as Geometric Sequence.

• A sequence can be arithmetic, when there is a common difference between successive terms, indicated as ‘d’. On the contrary, when there is a common ratio between successive terms, represented by ‘r’, the sequence is said to be geometric.

• In an arithmetic sequence, the new term is obtained by adding or subtracting a fixed value to/from the preceding term. As opposed to, geometric sequence, wherein the new term is found by multiplying or dividing a fixed value from the previous term.

• In an arithmetic sequence, the variation in the members of the sequence is linear. As against this, the variation in the elements of the sequence is exponential.

• The infinite arithmetic sequences, diverge while the infinite geometric sequences converge or diverge, as the case may be.

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