CAT QA SEQUENCE SERIES QUESTIONS

A lab experiment measures the number of organisms at 8 am every day. Starting with 2 organisms on the first day, the number of organisms on any day is equal to 3 more than twice the number on the previous day. If the number of organisms on the  day exceeds one million, then the lowest possible value of  is

Three positive integers x, y and z are in arithmetic progression. If y − x > 2 and xyz = 5(x + y + z), then z − x equals

Let the m-th and n-th terms of a geometric progression be 3/4 and 12 , respectively, where m<n. If the common ratio of the progression is an integer r, then the smallest possible value of r + n - m is

A gentleman decided to treat a few children in the following manner. He gives half of his total stock of toffees and one extra to the first child, and then the half of the remaining stock along with one extra to the second and continues giving away in this fashion. His total stock exhausts after he takes care of 5 children. How many toffees were there in his stock initially?

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

If the population of a town is p in the beginning of any year then it becomes 3+2p in the beginning of the next year. If the population in the beginning of 2019 is 1000, then the population in the beginning of 2034 will be

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Let a1, a2, ... , a52 be positive integers such that a1 ＜ a2 ＜ ... ＜ a52. Suppose, their arithmetic mean is one less than the arithmetic mean of a2, a3, ..., a52. If a52 = 100, then the largest possible value of a1 is

Let t1, t2,… be real numbers such that t1+ t2 +... + tn = 2n2 + 9n + 13, for every positive integer n ≥ 2. If tk=103, then k equals (TITA)

The value of the sum 7 x 11 + 11 x 15 + 15 x 19 + ..... + 95 x 99 is

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

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 [TITA]

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

If p^th term of a geometric progression is q and q^th term of same geometric progression is q, then find the product of (p-1)^th term and (q+1)^th term of same geometric progression.

In a certain infinite geometric series, the sum ofany 3 consecutive terms equals 7 times sum of all terms that follow them. Find the ratio of any term to the sum of all the terms that follow them.

a, b and c are three positive integers such that a+b+c = 36 such that a,b and c are A.P. while 3a, 4b and 6c are in G.P. What is the value of c?

Sum of an infinite G.P. is 192. Sum of the first n terms of the same G.P. is 189. How many rational values are possible for the common ratio of this G.P.?

Sum of the first 6 terms of an A.P. is 9. If the first term is 6 times the third term, find the value of the fifth term.

In a G.P. ,    T_n – T_n-1= constant (23T₁₆ + 27T₁₂) : ( 18T₁₇ + 7T₂₁) ?

Find the sum of 50 terms of the series 1 + (1+ 3) + (1 + 3 + 5) +... .

There are six positive integers, p, q, r, s, t, and u such that their sum is 12 and product is 64. What is the maximum possible value of pqrs + pqrt + pqru + ... + qstu + rstu?

A team of eleven cricketers is standing in a row and not all of them have the same number of balls with them. If the first cricketer distributes his balls among the remaining ten cricketers such that he doubles their respective number of balls, then he will be left with 3 balls. Instead, if the second cricketer takes away 4 balls from each of the remaining ten cricketers, then the number of balls with him will be two less than the number of balls that the first cricketer initially had. Find the sum of the number of balls available with the third, fourth, ......eleventh cricketer.

There are 5984 steel balls stacked in a pile with one ball on the top, 3 balls in the second layer, 6 balls in the third layer, 10 balls in the 4th layer, and so on. Find the total number of layers.

A sequence of 1000 numbers is in AP with a common difference of 3 between successive terms. The sum of all the terms of the AP is 10000. What is the sum of every fourth term of the same AP, starting with the first term and ending with the fourth last term?

A child starts writing the series a, a, b, a, b, c, a, b, c, d, a, b, c, d, e ....and so on. What will be the 250th letter she writes?

Santa starts with the number 80, triples it, and then adds 2. He repeats this procedure 101 more times, each time starting with the number from the previous result. The final result can be written as 9p – 1, where p is a natural number. Find the value of p.