Quantitative Aptitude - Modern Maths - Progressions - If a1 = 1/(2*5), a2 = 1/(5*8) Quantitative Aptitude - Modern Maths - Progressions Question If a1 = 1/(2*5), a2 = 1/(5*8), a3 = 1/(8*11),……, then a1 + a2 +……..+ a100 is A) 25/151 B) 1/2 C) 1/4 D) 111/55 Answer Option (A) Solution From CAT 2017 - Quantitative Aptitude - Modern Maths - Progressions, we can see that, The 100th term will be 1/299*302 The series is: 1/(2*5) + 1/(5*8) + 1/(8*11) + ……………+ 1/(299*302) It can also be written as 3[1/2 �

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Quantitative Aptitude - Modern Maths - Progressions - An infinite GP a1, a2, a3,.... Quantitative Aptitude - Modern Maths - Progressions Question An infinite geometric progression a1, a2, a3,... has the property that an = 3(a(n+ l) + a(n+2) +….) for every n ≥ 1. If the sum a1 + a2 + a3 +….... = 32, then a5 is A) 1/32 B) 2/32 C) 3/32 D) 4/32 Answer Option (C) Solution From CAT 2017 - Quantitative Aptitude - Modern Maths - Progressions, we can see that, For any n ≥ 1, an = 3 (a(n+1) + a(n+2) + ……..) So, a1 =

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Quantitative Aptitude - Modern Maths - Progressions - Let a1, a2, a3, a4, a5 Quantitative Aptitude - Modern Maths - Progressions Question Let a1, a2, a3, a4, a5 be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with 2a3. If the sum of the numbers in the new sequence is 450, then a5 is Answer 51 Solution From CAT 2017 - Quantitative Aptitude - Modern Maths - Progressions, we can see that, 5 consecutive odd numbers are a1 , a2 , a3 , a4 , a5. 5 consecutive even number

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Quantitative Aptitude - Modern Maths - Progressions - Let a1, a2,……..a3n be an arithmetic progression Quantitative Aptitude - Modern Maths - Progressions Question Let a1, a2,……..a3n be an arithmetic progression with a1 = 3 and a2 = 7. If a1 + a2 + ….+a3n = 1830, then what is the smallest positive integer m such that m (a1 + a2 + …. + an ) > 1830? A) 8 B) 9 C) 10 D) 11 Answer Option (B) Solution From CAT 2017 - Quantitative Aptitude - Modern Maths - Progressions, we can see that, a = 3 a + d = 7 => d=4 Apply

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Quantitative Aptitude - Modern Maths - Progressions - If the square of the 7th term Quantitative Aptitude - Modern Maths - Progressions Question If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is A) 2 : 3 B) 3 : 2 C) 3 : 4 D) 4 : 3 Answer Option (A) Solution From CAT 2017 - Quantitative Aptitude - Modern Maths - Progressions, we can see that, (a+6d)^2 = (a+2d)(a+16d) a^2 + 12

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Quantitative Aptitude – Modern Maths - Progressions – Let a(base1), a(base2) Slot -2 – Quantitative Aptitude – Modern Maths - Progressions – Let a(base1), a(base2), ...a(base52)  Let a(base1), a(base2), ... , a(base52) be positive integers such that a(base1) < a(base2) < ... < a(base52). Suppose, their arithmetic mean is one less than the arithmetic mean of a(base2), a(base3), ..., a(base52). If a(base52) = 100, then the largest possible value of a(base1) is? a) 45 b) 20 c) 48 d) 23 Answer: d) 23

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Quantitative Aptitude – Modern Maths - Progressions – The arithmetic mean of x, y Slot -2 – Quantitative Aptitude – Modern Maths - Progressions – The arithmetic mean of x, y The arithmetic mean of x, y and z is 80, and that of x, y, z, u and v is 75, where u=(x+y)/2 and v=(y+z)/2. If x ≥ z, then the minimum possible value of x is? Answer: 105 Solution: Given, (x+y+z)/3=80 x+y+z=240------1) And (x+y+z+u+v)/4=75 x+y+z+u+v =375------2) From eq 1) & eq 2) u+v =135 And from question , u+v =(x+2y+z)/2 O

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Quantitative Aptitude – Modern Maths - Progressions – Let x, y, z be three positive real Slot -1 – Quantitative Aptitude – Modern Maths - Progressions – Let x, y, z be three positive real numbers Let x, y, z be three positive real numbers in a geometric progression such that x < y < z. If 5x, 16y, and 12z are in an arithmetic progression then the common ratio of the geometric progression is? a) 5/2 b) 1/6 c) 3/2 d) 3/6 Solution: Given x,y, z are in GP . let common ratio of this GP is r so y=xr & z=x

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