One of the most crucial elements of your **online CAT preparation** is practicing questions from **CAT previous year paper** to set yourself up for the tricky questions the **CAT Question Paper** throws at you. You can find yourself stuck in trickier topics like Progressions and hence practicing CAT previous year paper for these topics becomes even more important. Here is a question on progressions from CAT 2020 question paper. Try your hands at this questions and see if you can easily steer through.

To solve more questions on Progressions, visit **2IIM's Question Bank**.

Question 6 : Let the m-th and n-thterms of a Geometric progression be \\frac{3}{4}) and 12, respectively, when m < n. If the common ratio of the progression is an integer r, then the smallest possible value of r + n - m is

- -4
- -2
- 6
- 2

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\\frac{3}{4}) 12

mth nth

m > n

Given r is an integer, So r^{k} = \\frac{12}{\frac{3}{4}}) = 16

r^{k} = 2^{4} or 4^{2}

Since asked for minimum possible value, Taking r^{k} = {(-2)}^{2} or {(-4)}^{2}

k = n – m (From m how many terms we have to jump to reach n)

We have two cases r = - 2 and n - m = 4 ----> r + n – m = 2

r = - 4 and n – m = 2 ----> r + n – m = - 2

-2 is the smallest possible value

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