Hello Friends!
Under this post " Number System: Arithmetic Progression and Geometric Progression " we will see arithmetic progression and geometric progression, formula used for AP and GP and types of questions asked in competitive exams.
1) Geometric Progression / Geometric Series / Geometric Sequence : x, xr, xr2, xr3, xr4, --- are said to be in geometric progression. Here, a is first term and r is common ratio.
a) nth term = xr (n -1)
b) Sum of n terms = | x (1 – rn) | , here r < 1 |
(1 – r) |
c) Sum of n terms = | x (rn – 1) | , here r > 1 |
(r – 1) |
2) Arithmetic Progression / Arithmetic Series / Arithmetic Sequence : x, x + y, x + 2y, x + 3y are said to be in A.P. Here x is first term and common difference is y.
a) nth term = x + (n – 1) y
b) Sum of n terms = | n | [2x + (n – 1)y] |
2 |
3) 1 + 2 + 3 +- - - - + n = | n(n + 1) |
2 |
4) (12 + 22 + 32 - - - - + n2) = | n(n + 1) (2n + 1) |
6 |
5) (13 + 23 + 33 - - - - + n3) = | ![]() | n(n + 1) | ![]() | 2 |
2 |
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