CAT 2017 Question Paper | Quants Slot 2

The best questions to practice for CAT Exam are the actual CAT Question Papers. 2IIM offers you exactly that, in a student friendly format to take value from this. If you would like to take the same inside a testing engine (for Free) head out here: CAT Official Question Mocks. In CAT 2017 we saw some beautiful questions that laid emphasis on Learning ideas from basics and being able to comprehend more than remembering gazillion formulae and shortcuts. Original CAT Question paper is the best place to start off your CAT prep practice. This page provides exactly that. To check out about 1000 CAT Level questions with detailed video solutions for free, go here: CAT Question Bank

Question 33 : An infinite geometric progression a₁, a₂, a₃,... has the property that a_n = 3(a_n+1 + a_n+2 +....) for every n ≥ 1. If the sum a₁ + a₂ + a₃ +...... = 32, then a₅ is

1. \\frac{1}{32})
2. \\frac{2}{32})
3. \\frac{3}{32})
4. \\frac{4}{32})

Video Explanation

Explanatory Answer

Method of solving this CAT Question from Progressions

The sum up to infinity, a₁ + a₂ + a₃ +...... = 32.
It can also be written as \\frac{𝑎}{1 − 𝑟}) = 32.
We have been given that, a_n = 3(a_n+1 + a_n+2 +....) if n ≥ 1.
When n = 1, we get,
a = 3(a₂ + a₃ + .....)
⟹ a = \\frac{3𝑎𝑟}{1 − 𝑟}) [Since, a₂ + a₃ +...... = \\frac{𝑎r}{1 − 𝑟})]
⟹ 1 – r = 3r
⟹ 1 = 4r
⟹ r = \\frac{1}{4})
Now finding the value of a is easy.
a = 32 × (1 - \\frac{1}{4}))
⟹ a = 32 × \\frac{3}{4})
⟹ a = 24
The value of a₅ = ar⁴ , where a = 24 and r⁴ = (\\frac{1}{4}))⁴
a₅ = 24 × \\frac{1}{4}) × \\frac{1}{4}) × \\frac{1}{4}) × \\frac{1}{4})
Hence a₅ = \\frac{3}{32})

The question is "An infinite geometric progression a₁, a₂, a₃,... has the property that a_n = 3(a_n+1 + a_n+2 +....) for every n ≥ 1. If the sum a₁ + a₂ + a₃ +...... = 32, then a₅ is"

Hence, the answer is \\frac{3}{32})

Choice C is the correct answer