An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference “d”
For example, the sequence 9, 6, 3, 0,-3, …. is an arithmetic progression with -3 as the common difference. The progression -3, 0, 3, 6, 9 is an Arithmetic Progression (AP) with 3 as the common difference.
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n – 1) d, where Tn = nth term and a = first term. Here d = common difference = Tn – Tn-1.
Sum of first n terms of an AP: S =(n/2)[2a + (n- 1)d]
The sum of n terms is also equal to the formula S(n) = n/2(a+1) where l is the last term.
Tn = Sn – Sn-1 , where Tn = nth term
When three quantities are in AP, the middle one is called as the arithmetic mean of the other two. If a, b and c are three terms in AP then b = (a+c)/2
A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio. For example, the sequence 4, -2, 1, - 1/2,.... is a Geometric Progression (GP) for which - 1/2 is the common ratio. The…
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Let A₁, A₂, …, An, n arithmetic means are inserted between two numbers ‘a’ and ‘b’ such that a, A₁, A₂, …, An, b from an AP. Here, total number of terms are (n + 2) and common difference be d b = (n + 2)th term = a +…
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