This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 ; : : : :...
View
Full Document
 Spring '09
 Dr.RajaLatif
 Math, Geometric Series, Time Value Of Money, Annual Percentage Rate, Geometric progression

Click to edit the document details