10.2 "Arithmetic Sequences"
"common difference"
Arithmetic Sequence: ak+1 = ak + d
Solve for d: d = ak+1 ­ ak (the common difference)
(ex) ak = 8 , d = 3
8, 11, 14, 17, 20, ...
(ex) Show that the sequence is arithmetic, & find the common difference.
53, 48, 43, ..., 58 ­ 5n, ...
nth term of an arithmetic sequence: an = a1 + (n ­ 1)d
(ex) 10, 14, 18, 22, ...
Find the nth term, the 5th term, & the 10th term of the arithmetic sequence.
(ex) 16, 13, 10, 7, ...
(ex) ­6, ­4.5, ­3, ­1.5, ...
(ex) x­8, x­3, x+2, x+7, ...
(ex) log 1000, log 100, log 10, log 1, ...
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(ex) Find the common difference.
a4 = 14, a11 = 35
Find the specified term given the 2 terms.
(ex) a11 ; a1 = 2 + √2 , a2 = 3
(ex) a1 ; a8 = 47 , a9 = 53
(ex) a10 ; a2 = 1 , a18 = 49
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Little Guass: 1+2+3+4+... +97+98+99+100
How about: 10+13+16+19+22+25
How about: 10+20+30+40+50+60+70
Formulas to find the sum of an arithmetic sequence:
Find the sum Sn of the arithmetic sequence that satisfies the stated conditions.
(ex) a1 = 5 , d = 0.1 , n = 40 (Use both formulas on this one.)
(ex)
Find the sum.
(ex)
(ex)
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Express the sum in terms of summation notation.
(ex) 3 + 8 + 13 + 18 + 23
(ex) 3 + 8 + 13 + ... + 463
(ex) (ex) 2 + 11 + 20 + ... + 16,058 (also find the sum)
Find the number of terms in the arithmetic sequence with the given conditions. (ex) a1 = ­1 , d = 1/5 , S = 21
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Stadium Seating. The first ten rows of seating in a certain section of a stadium have 30 seats, 32 seats, 34 seats, and so on. The eleventh through the twentieth rows each contain 50 seats. Find the total number of seats in the section.
Coasting Downhill. A bicycle rider coasts downhill, traveling 4 feet the first second. In each succeeding second, the rider travels 5 feet farther than in the preceding second. If the rider reaches the bottom of the hill in 11 seconds, find the total distance traveled.
Sales Bonuses. A company is to distribute $46,000 in bonuses to its top ten salespeople. The tenth salesperson on the list will receive $1000, and the difference in bonus money between successively ranked salespeople is to be constant. Find the bonus for each salesperson.
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