📝Geometric Progressions
➤ A sequence `a_1, a_2, a_3 ..., a_n....` is called geometric progression, if each term is non-zero and `a_{k+1}/a_k = r` (constant), `∀ k geq1`
By letting `a_1 = a`, where `a = 1^{st}` term and `r` is called the common ratio.
`n^{th}` term of a G.P.
Let first non-zero term `‘a’` and common ratio `‘r’`.
`1^{st}` term `= a_1 = a = ar^{1-1}`
`2^{nd}` term `= a_2 = ar = ar^{2-1}`
`3^{rd}` term `= a_3 = a_2r = ar×r = ar^2 = ar^{3-1}`
`4^{th}` term `= a_4 = a_3r = ar^2×r = ar^3 = ar^{4-1}`
`therefore` the pattern suggests that the `n^{th}` term of a G.P. is given by
`a_n = ar^{n-1}`
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