diffrence between AP and GP?????
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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 = 2).
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).
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)
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 = 2).
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).
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)
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Answer:
ap -arithmetic progression
gp -geometric progression
In an AP series the common difference between the terms are equal. That is 0,2,4,6,8… here common difference between the terms is 2. In GP the terms have a common ratio.
Step-by-step explanation:
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