Algebra 2 Arithmetic Series

Algebra 2 Series – is the expression for the sum of the terms of a sequence.

Algebra 2 Series – is the expression for the sum of the terms of a sequence. Finite - sequences and series have terms that you can count individually from 1 to a final whole number.

Algebra 2 Series – is the expression for the sum of the terms of a sequence. Finite - sequences and series have terms that you can count individually from 1 to a final whole number. Infinite sequences and series continue without end. You indicate an infinite sequence or series with ellipsis points.

Algebra 2 Series – is the expression for the sum of the terms of a sequence. Finite - sequences and series have terms that you can count individually from 1 to a final whole number. Infinite sequences and series continue without end. You indicate an infinite sequence or series with ellipsis points. Finite SequenceFinite Series 6,9,12,15, Infinite SequenceInfinite Series 3,7,11,15,… …

Algebra 2 Arithmetic Series Lesson 11-4 Use the finite sequence 5, 9, 13, 17, 21, 25, 29. Write the related series. Evaluate the series. Additional Examples

Algebra 2 Arithmetic Series Lesson 11-4 Use the finite sequence 5, 9, 13, 17, 21, 25, 29. Write the related series. Evaluate the series. The sum of the terms of the sequence is = 119 Related seriesAdd to evaluate. Additional Examples

Algebra 2 Arithmetic Series – is a series whose terms form an arithmetic sequence. When a sequence has many terms or when you know only the first and last terms of the sequence, you can use a formula to evaluate the related series quickly

Algebra 2 Arithmetic Series – is a series whose terms form an arithmetic sequence. When a sequence has many terms or when you know only the first and last terms of the sequence, you can use a formula to evaluate the related series quickly To find the sum of a certain number of terms of an arithmetic sequence: where S n is the sum of n terms (n th partial sum), a 1 is the first term, a n is the n th term.

Algebra 2 Arithmetic Series Lesson 11-4 A staircase uses same-size cement blocks arranged 4 across, as shown below. Find the total number of blocks in the staircase. Additional Examples

Algebra 2 Arithmetic Series Lesson 11-4 A staircase uses same-size cement blocks arranged 4 across, as shown below. Find the total number of blocks in the staircase. Relate: sum of the series is number of terms 2 times the first term plus the last term Define:Let S n = total number of blocks, and let n = the number of stairs. Then a 1 = the number of blocks in the first stair, and a n = the number of blocks in the last stair. Additional Examples

Algebra 2 Arithmetic Series Lesson 11-4 (continued) = 2.5(24)Simplify. = 60Multiply. There are 60 blocks in the stairs. n2n2 Write: S n = ( a 1 + a n ) Use the formula. = (4 + 20)Substitute n = 5, a 1 = 4, a n = Additional Examples

Algebra 2 Arithmetic Series Lesson 11-4 Additional Examples A series can be represented in a compact form, called summation notation, or sigma notation. The Greek capital letter sigma,  is used to indicate a sum.

Algebra 2 Arithmetic Series Lesson 11-4 Use the series (–2n + 3). Evaluate the series  4 n = 1 Additional Examples

Algebra 2 Arithmetic Series Lesson 11-4 Use the series (–2n + 3). Evaluate the series  4 n = 1 Additional Examples

Algebra 2 Arithmetic Series Lesson 11-4 Additional Examples Use the summation notation to write the series for 50 terms.

Algebra 2 Arithmetic Series Lesson 11-4 Additional Examples Use the summation notation to write the series for 50 terms. 8 1 = 8, 8 2 = 16, 8 3 = 24,... The explicit formula for the sequence is 8n.

Algebra 2 Arithmetic Series Lesson 11-4 Additional Examples Use the summation notation to write the series for 50 terms. 8 1 = 8, 8 2 = 16, 8 3 = 24,... The explicit formula for the sequence is 8n = 8n The lower limit is 1 and the upper limit is 50.  50 n = 1

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