LrAnnuityOrdinaryChVSIII - Dr. Raja Latif. Finite...

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Dr. Raja Latif. Finite Mathematics.Pg:1 Dr. Raja Latif. 5.3 ANNUITIES Objective : To introduce the notions of ordinary annuities 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 infinite list of numbers a , ar , ar 2 , ar 3 , ar 4 ,... is called a geometric sequence. The number a is called the first term of the sequence, 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 first 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 1, multiply both sides of the equation by r to get rS n ar ar 2 1
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Dr. Raja Latif. Finite Mathematics.Pg: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 first term is a and common ratio is r is given by S n a r n 1 1 r , r 1. ExampleLGR217. Find the sum of the first six terms of
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LrAnnuityOrdinaryChVSIII - Dr. Raja Latif. Finite...

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