Question

Definition of arithmetic and geometric progression

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

A sequence of numbers is called an arithmetic progression if the difference between any two consecutive terms is always same. In simple terms, it means that next number in the series is calculated by adding a fixed number to the previous number in the series. This fixed number is called the common difference.

For example, 2,4,6,8,10 is an AP because difference between any two consecutive terms in the series (common difference) is same (4 – 2 = 6 – 4 = 8 – 6 = 10 – 8 = GP?) .

If ‘a’ is the first term and ‘d’ is the common difference,

nth term of an AP = a + (n-1) d

Arithmetic Mean = Sum of all terms in the AP / Number of terms in the AP

Sum of ‘n’ terms of an AP = 0.5 n (first term + last term) = 0.5 n [ 2a + (n-1) d ]

Geometric Progression (GP)

A sequence of numbers is called a geometric progression if the ratio of any two consecutive terms is always same. In simple terms, it means that next number in the series is calculated by multiplying a fixed number to the previous number in the series. This fixed number is called the common ratio.

For example, 2,4,8,16 is a GP because ratio of any two consecutive terms in the series (common difference) is same (4 / 2 = 8 / 4 = 16 / 8 = 2).

If ‘a’ is the first term and ‘r’ is the common ratio,

nth term of a GP = a rn-1

Geometric Mean = nth root of product of n terms in the GP

Sum of ‘n’ terms of a GP (r < 1) = [a (1 – rn)] / [1 – r]

Sum of ‘n’ terms of a GP (r > 1) = [a (rn – 1)] / [r – 1]

Sum of infinite terms of a GP (r < 1) = (a) / (1 – r)