Download Arithmetic Sequence in Mathematics and more Study notes Mathematics in PDF only on Docsity! MATHEMATICS: ARITHMETIC SEQUENCE This module aims the learners to understand: 1. Arithmetic Sequence 2. How to get the Common Difference 3. How to solve for Arithmetic Sequence 4. Determine if the sequence is Arithmetic or not Arithmetic Sequence- Also known as Arithmetic Progression, is a sequence of numbers where the difference between any two consecutive terms remains the same. This consistent difference is referred to as the common difference, represented by โdโ. To obtain each term in the sequence, you simply add the common difference to the previous term. 4 11 18 25 (aโ) (aโ) (aโ) (aโ) โ Example of Arithmetic Sequence: 2, 6, 10, 14, 18 โ added by 4 2, 5, 8, 11, 14 โ added by 3 Common Difference: refers to the fixed amount by which consecutive terms in a sequence increase or decrease. It is a fundamental concept in arithmetic sequences, where each term is obtained by adding or subtracting the same value from the previous term. Equation for COMMON DIFFERENCE: d = aโ + aโ Finite Sequence: 5, 10, 15, 20, 25 โ has a clear starting & stopping point Infinite Sequence: 5, 10, 15, 20, 25โฆ (...)โ Ellipsis, goes on forever Ex. 1. 4, 9, 14, 19, 24 2. 13, 6, -1, -8โฆ 1st term: aโ = 4 1st term: aโ = 13 n = 5 ( 5 terms) d = aโ - aโ d = aโ - aโ โ d = 6 - (-13) d = 9 - 4 d = -7 d = 5 Equation for ARITHMETIC SEQUENCE: An = Aโ + ( n - 1 ) d Anโ Looking for n Aโ โ First term ( n - 1 )โ term number / number of term in a sequence dโ common difference Ex. 1. Find the 14th term of AS 4, 7, 10, 13. Aโโ = Aโ + ( n - 1 ) d d = aโ - aโ Aโโ = 4 + ( 14 - 1 ) 3 . d = 7 - 4 Aโโ = 4 + ( 13 ) 3 . d = 3 Aโโ = 4 + 39 Aโโ = 43 2. 15th term of AS with the 1st term of 5, and d is -6. Aโโ
= ? aโ = 5 d = -6 Aโโ
= Aโ + ( n - 1 ) d Aโโ
= 5 + ( 15 - 1 ) -6 Aโโ
= 5 + ( 14) -6 Aโโ
= 5 + (-84) Aโโ
= -79
