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Algebra -4- Arithmetic Progression || Quantitative Aptitude || CAT 2021 || 06 May (App update required to attempt this test)

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Question 1

In an arithmetic progression, if the ratio of the ( r + 2) th term and the ( r + 5) th term is ( r + 3) : ( r + 6) and the sum of the first 4r terms and the sum of the first 7r terms are in the ratio 1 : 3, find the value of f(x) at x = r , if f(x) = x2 – 1 .

Question 2

Let Um denote the sum of the first m natural numbers. For how many values of m less than or equal to 100, is Um is divisible by 15? (TITA)

Question 3

If the 16th term of an Arithmetic Progression (a) is 1/2 times the 20th term of another Arithmetic Progression (b) then the sum of the first 31 terms of AP (a) is how many times the sum of the first 39 terms of AP (b)?

Question 4

In how many ways can 350 be written as sum of five terms of an Arithmetic Progression (AP), such that all the five terms of the AP are positive integers?

Question 5

If the arithmetic mean of (80)9 and (80)16 is (40)n then the value of n is ?

Question 6

The number of integers between 300 and 1100 which are divisible by either 7 or 13 but not both is

Question 7

In two Arithmetic progressions P and Q , their respective first terms are x and y where x : y = 2 : 5 and their common differences are m and n respectively. If the sum of first five terms of these APs are in the ratio of 1:2 respectively, find the value of .(TITA) (Write the answer in decimal expansion)

Question 8

The sum of first p term of an Arithmetic Progression (S1) is and the sum of first n terms of another Arithmetic Progression (S2) is . Which two terms of the two APs’ will give sum 40?

Question 9

An arithmetic progression of natural numbers has sum of the first and the tenth term as 46, if first term is less than 8, what is the sum of first 25 terms of that progression?

Question 10

The number of common terms in the two sequences: 15, 19, 23, 27, ...... , 415 and 14, 19, 24, 29, ...... , 464 is
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