(11C) n-th term of a Geometric Sequence
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05-21-2018, 09:31 AM
(This post was last modified: 05-22-2018 11:52 AM by Gamo.)
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(11C) n-th term of a Geometric Sequence
Nth term of a Geometric Sequence giving
Initial Value (a) Common Ratio (r) Term (n) Formula: a sub n = ar^n-1 for every integer n ≥ 1 More information about Geometric Progression: https://en.wikipedia.org/wiki/Geometric_progression Example: a=2 r=3.14 n=14 Procedure: Set User Mode 2 A > 2 // Input initial value 3.14 B > 3.14 // Input common ratio 14 C > 14 // Input term D > 5769197.69 // answer on the 14th term What is the sequence number on the 1st and 2nd term on the above example? (1st Term) 1 C > D > 2 (2nd Term) 2 C > D > 6.28 The sequence are 2, 6.28, 19.72, 61.92,....... Program: Code:
Remark: The common ratio of a geometric sequence may be negative, resulting in an alternating sequence, with numbers switching from positive to negative and back. For instance 1, −3, 9, −27, 81, −243, ... is a geometric sequence with common ratio −3. Input 1 A, -3 B, and your choice of term [C] then [D] for answer. ------------------------------------------------------------------------------ This update version can be use for the following: LBL A // To display a geometric progression LBL B // To find from the n-th term LBL C // To find the sum of the giving n-th term Procedure: For geometric sequence: (a) ENTER (r) > f [A] > continue [R/S] For n-th term: (a) ENTER (r) ENTER (n) > f [B] For the Sum of given n-th term: (a) ENTER (r) ENTER (n) > f [C] Example: a=1 r= -3 n= selected term Sequence: 1, -3, 9, -27, 81, -243,...... Geometric Sequence: 1 ENTER -3 f [A] > 1 > [R/S] > -3 > [R/S] > 9 4th term: 1 ENTER -3 ENTER 4 f [B] > -27 Sum to 4th term: 1 ENTER -3 ENTER 4 f [C] > -20 Program: Code:
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(11C) n-th term of a Geometric Sequence - Gamo - 05-21-2018 09:31 AM
RE: (11C) n-th term of a Geometric Sequence - Dieter - 05-21-2018, 12:47 PM
RE: (11C) n-th term of a Geometric Sequence - Gamo - 05-21-2018, 03:42 PM
RE: (11C) n-th term of a Geometric Sequence - Dieter - 05-21-2018, 04:06 PM
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