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Unformatted text preview: 1 Dr. Raja Latif. Math 131.5.3 ANNUITIES Objective: To introduce the notions of ordinary an nuities and annuities due. To use geometric series to model the present value and future value of an annuity. Geometric Sequence: If a and r are nonzero real numbers, the in&nite list of numbers a; ar; ar 2 ; ar 3 ; ar 4 ; : : : is called a geometric sequence. The number a is called the &rst term of the se quence, ar is the second term, ar 2 is the third term, and so on. Thus for any n & 1 ; ar n ¡ 1 is the nth term of the sequence. Each term in the sequence is r times the preceding term. The number r is called the common ratio of the sequence. The sum S n of the &rst n terms of the geometric sequence is called the geometric series: S n = a + ar + ar 2 + ar 3 + ar 4 + : : : + ar n & 1 : ( ¡ ) If r = 1 ; then S n = a + a + a + a + : : : + a = na: If r 6 = 1 ; multiply both sides of the equation by r to get rS n = ar + ar 2 + ar 3 + ar 4 + : : : + ar n : ( ¡¡ ) Now subtract corresponding sides of equation ( ¡ ) from equation ( ¡¡ ) : rS n = ar + ar 2 + ar 3 + ar 4 + : : : + ar n S n = & & ar + ar 2 + ar 3 + ar 4 + ::: + ar n & 1 ¡ rS n & S n = & a + ar n = ) S n ( r & 1) = a ( r n & 1) = ) S n = a ( r n & 1) r & 1 : Sum of Geometric Series: The sum s of a geometric series of n terms whose &rst term is a and common ratio is r is given by S n = a ( r n & 1) 1 & r ; r 6 = 1 : ExampleLGR217. Find the sum of the &rst six terms of the geometric sequence 3 ; 12 ; 48 ; : : : :...
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 Spring '09
 Dr.RajaLatif
 Math, Geometric Series

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