# 5 - Sequence and Series Questions Answers

Between two numbers, whose sum is 13/6, an even number of arithmetic means are inserted, the sum of these means exceed their number by unity. How many means are there?

**Asked By: PREM**

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**Joshi sir comment**

**Asked By: PREM**

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**Joshi sir comment**

Find Sum to n terms

x/1-x² + x²/1-x⁴ + x⁴/1-x⁸ + ....

**Asked By: LUFFY**

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**Joshi sir comment**

$\frac{x}{1-{x}^{2}}=\frac{1}{1-x}-\frac{1}{1-{x}^{2}}\phantom{\rule{0ex}{0ex}}breakalltermssimilarlyandsolve\phantom{\rule{0ex}{0ex}}$

The sum of three positive real numbers x, y and z is 9. If the largest positive difference between any 2 of the 3 numbers is 5 and these 3 numbers are in arithmetic progression then the product of these 3 numbers will be what .please tell me.

**Asked By: S.NANDHINI**

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**Joshi sir comment**

let the numbers are a-d, a, a+d

then according to the given condition a-d+a+a+d = 9 so 3a = 9 so a = 3

and [a+d]-[a-d] = 5 so 2d = 5 so d =5/2

now solve

The AM of two positive numbers a & b exceeds their GM by 3/2 & the GM exceeds the HM by 6/5 such that a+b= α , |a-b|=β , then which of them are correct,

1) α + β² = 96 2) α + β² =74 3)α²+β = 234 4)α²+β = 84

**Asked By: AMIT DAS**

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**Joshi sir comment**

(a+b)/2 = √ab + 3/2 (1) or a+b = 2√ab + 3

√ab = 2ab/(a+b) + 6/5 (2) or 5(a+b)√ab = 10ab + 6(a+b)

on solving these 2 we get 5[2√ab + 3]√ab = 10ab + 6[2√ab + 3]

or 10ab + 15√ab = 10ab + 12√ab + 18

or 3√ab = 18 or ab = 36 and a+b = 15 = α

so a-b = √(225 - 144) = √81 = 9 = β