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7. (In a certain A.P, the sum of the second, third and seventh terms is 32 and the sum of the first six terms is 36. Find the first term and the common difference of the progression. Find also the minimum value ofn for which the sum of the first n terms exceeds 1.000.

7. (In a certain A.P, the sum of the second, third and seventh terms is 32 and the sum of the first six terms is 36. Find the first term and the common difference of the progression. Find also the minimum value ofn for which the sum of the first n terms exceeds 1.000.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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7. ( In a ceriain A.P, the sum of the second, third and seventh terms is 32 and the sum of the first six terms is 36. Find the first term and the common difference of the progression. Find also the minimum value of n for which the sum of the first n terms exceeds 1.000. o (ii} A convergent geometric series is such that the sum of all the ierms after the nth term is 3 times the nth term. Find the common ratio of the progression. Given that the first term of the progression isa, show that the sum to infinity is 4a and find, in terms of a, the geometric mean of the third and sixth terms. 8. The sum Sn of the first n terms of a series is given by S, ="(3n + 1). Show that the series is an arithmetic series, V Given that f(r) = r(r+1)(r+2), simplify f(r)- f(r -1). Hence deduce that: E-1r(r + 1) =n+1)(n+2). Prove this result by using mathematical induction %3D
Transcribed Image Text:7. ( In a ceriain A.P, the sum of the second, third and seventh terms is 32 and the sum of the first six terms is 36. Find the first term and the common difference of the progression. Find also the minimum value of n for which the sum of the first n terms exceeds 1.000. o (ii} A convergent geometric series is such that the sum of all the ierms after the nth term is 3 times the nth term. Find the common ratio of the progression. Given that the first term of the progression isa, show that the sum to infinity is 4a and find, in terms of a, the geometric mean of the third and sixth terms. 8. The sum Sn of the first n terms of a series is given by S, ="(3n + 1). Show that the series is an arithmetic series, V Given that f(r) = r(r+1)(r+2), simplify f(r)- f(r -1). Hence deduce that: E-1r(r + 1) =n+1)(n+2). Prove this result by using mathematical induction %3D
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