1. The first three terms of a GP are 1, x, y and the first 3 terms of an AP are 1, x, - y. Prove that x^2 + 2x - 1 = 0, and hence find y, given that x is positive. 2. Show that for an AP with first term a, common difference d and sum S, the number of terms n, must satisfy the quadratic equation given below. Find n when a = 3, d = ½, and S = 2828. Show derivation in your solutions and write the value of n in this form that will satisfy the premises. (photo will be attached ) 3. The sum of three numbers in an A.P. is 12 and the sum of their cubes is 408. Find the terms. 4. A geometric progression has positive terms. The sum of the first six terms is nine times the sum of the first three terms. The seventh term is 320. Find the common ratio and the first term. Find the smallest value of n such that the sum to first n terms of the progression exceeds 10^6 . (Show complete solutions and write answers in this form as: r=___, a=____, n=___. e.g.: r=4, a=7, n=20)
1. The first three terms of a GP are 1, x, y and the first 3 terms of an AP are 1, x, - y. Prove that x^2 + 2x - 1 = 0, and hence find y, given that x is positive.
2. Show that for an AP with first term a, common difference d and sum S, the number of terms n, must satisfy the
3. The sum of three numbers in an A.P. is 12 and the sum of their cubes is 408. Find the terms.
4. A geometric progression has positive terms. The sum of the first six terms is nine times the sum of the first three terms. The seventh term is 320. Find the common ratio and the first term. Find the smallest value of n such that the sum to first n terms of the progression exceeds 10^6 . (Show complete solutions and write answers in this form as: r=___, a=____, n=___. e.g.: r=4, a=7, n=20)
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