Presentation on theme: "Example 1: Find the 10th term and the nth term for the sequence 7, 10, 13, … . Solution: Un= U10 ="— Presentation transcript:
1 Example 1:Find the 10th term and the nth term for the sequence 7, 10, 13, … .Solution:Un=U10 =
2 Example 2Find the three numbers in an arithmetic progression whose sum is 24 and whose product is 480.SolutionLet the three numbers be (a-d), a, (a+d) where d is the common difference.(a-d)(a)(a+d)=480(a-d) +a + (a+d) = 24Substituting a =8, we get3a = 24a = 8
19 Example 9A geometric series has first term 1 and the common ratio r, where r 1, is positive. The sum of the first five terms is twice the sum of the terms from the 6th to 15th inclusive. Prove that
23 Sum to infinity, S (or ) =The sum to infinity exists (the series converges or series is convergent) providedExample 10Determine whether the series given below converge. If they do, give their sum to infinity.G.P. with >1(a)Does not converge
26 Example 11A geometric series has first term a and the common ratioShow that the sum to infinity of the geometric progression isSolution(shown)
27 Example 12A geometric series has first term a and common ratio r. S is the sum to infinity of the series, T is the sum to infinity of the even-numbered terms (i.e ) of the series. Given that S is four times the value of T, find the value of r.common ratio r 2Given S = 4T, we have
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