2412 Pre-Calculus Chapter 12 Section 2 Arithmetic Sequences

Arithmetic Sequence A sequence where the elements can be found by adding the same number to previous terms 2, 5, 8, 11, ___, ___ The number that is added is called the difference d. d = 3

Example 1: Tell if each sequence is arithmetic and find d if possible. 4, 7, 10, 13, /3,2/3, 4/3, 8/3... 1, 4, 9, 16, 25.. Yes d = 3 No

Example 2: Write the first 4 terms and tell if you have an arithmetic sequence u n = (2 n )n u n = (n-1) u n = 5 – 2n 2, 8, 24, 64 No 1, 13, 25, 37 Yes d = 12 3, 1, -1, -3 Yes d= -2

Example 3: Write the first 5 terms of the arithmetic sequence u 1 = 8, d = 4 u 1 = 3, d = -5 u 1 = 34, d = 1/2 8,12, 16, 20, 24 3, -2, -7, -12, , 34.5, 35, 35.5, 36

Finding any Arithmetic term To find the n th term you can use the formula:

Example 4: Find the 25 th term of: 2, 6, 10,... a 1 = d = n =

Example 5: Find the 120 th term if a 1 = 625 d = -2 n =

Adding Arithmetic Sequences To find the sum of n terms you can use the formula:

Example 5: Find the sum of the first 50 terms if a 1 = 245 d = 7 n = a n =

A school auditorium is built with seats in rows A through X so that the first row contains 27 seats, the fifth row contains 33 seats. How many seats are in row B? How many seats are in row X? How many seats are in the Auditorium? Would a school build an auditorium with this many seats? 28 – you can’t have a fractional seat 61 – you can’t have a fractional seat 1056 No – not a good break point for fees