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Show this defined as aat a1, a2, a3,an form A.Pwhere a,9-5n. |
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Answer» Given an = 9-5nto know the series,a1 = 9-5(1) = 4a2 = 9-5(2) = 9-10 = -1a3 = 9-5(3) = 9-15 = -6a4 = 9-5(4) = 9-20 = -11 ......So the series is 4, -1, -6, -11 ...common difference d = a2 - a1 = -1-4 = -5So, the common difference d = -5 (we can check it by doing a3-a2, a4-a3 ... )when we do with the a3-a2 and a4-a3 too, we get the common difference d=-5So the {an} i.e, the series is in A.PThen, by usingSn = n/2 [2a +(n-1)d]In above Calculation,We got that a = 4, d = -5, n=15 (as per problem)*he wasnt mentioned that in question, he mentioned that in commentsS15 = 15/2 [ 2(4)+(15-1)(-5)]S15 = 15/2 [ 8+14(-5)]S15 = 15/2 (-70+8)S15 = 15/2 (-62)S15 = 15(-31)S15 = -465therefore the sum of the first 15 numbers on the series that we find out is -465 Thank You |
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