CAT Sequences and Series previous year questions

22 Sequences and Series questions from CAT 2021–2025 (Quant), each with its answer and a step-by-step solution.

• Q4In the set of consecutive odd numbers \1,3,5,ldots ,57\ , there is a number k such that the sum of all the elements…CAT 2025 Slot 1 · Quant · Sequences and Series
• Q8Let a_n be the n^textth term of a decreasing infinite geometric progression. If a_1+a_2+a_3=52 and…CAT 2025 Slot 2 · Quant · Sequences and Series
• Q2In an arithmetic progression, if the sum of fourth, seventh and tenth terms is 99, and the sum of the first fourteen…CAT 2025 Slot 3 · Quant · Sequences and Series
• Q14Suppose x_1,x_2,x_3,ldots ,x_100 are in arithmetic progression such that x_5=-4 and 2x_6+2x_9=x_11+x_13 . Then, x_100…CAT 2024 Slot 1 · Quant · Sequences and Series
• Q18For any natural number n , let a_n be the largest integer not exceeding √n . Then the value of a_1+a_2+cdots +a_50 isCAT 2024 Slot 1 · Quant · Sequences and Series
• Q8The sum of the infinite series (1)/(5) ( (1)/(5)-(1)/(7) )+ ( (1)/(5) )² ( ( (1)/(5) )²- ( (1)/(7) )² )+ ( (1)/(5) )³…CAT 2024 Slot 2 · Quant · Sequences and Series
• Q17Consider the sequence t_1=1 , t_2=-1 and t_n=(n-3)/(n-1)t_n-2 for n≥ 3 . Then, the value of the sum…CAT 2024 Slot 3 · Quant · Sequences and Series
• Q20For some positive and distinct real numbers x , y and z , if (1)/(√y+√z) is the arithmetic mean of (1)/(√x+√z) and…CAT 2023 Slot 1 · Quant · Sequences and Series
• Q22A lab experiment measures the number of organisms at 8 am every day. Starting with 2 organisms on the first day, the…CAT 2023 Slot 1 · Quant · Sequences and Series
• Q20Let both the series a_1 , a_2 , a_3 , ... and b_1 , b_2 , b_3 ... be in arithmetic progression such that the common…CAT 2023 Slot 2 · Quant · Sequences and Series
• Q22Let a_n and b_n be two sequences such that a_n=13+6 ( n-1 ) and b_n=15+7 ( n-1 ) for all natural numbers n . Then, the…CAT 2023 Slot 2 · Quant · Sequences and Series
• Q20The value of 1+ ( 1+(1)/(3) )(1)/(4)+ ( 1+(1)/(3)+(1)/(9) )(1)/(16)+ ( 1+(1)/(3)+(1)/(9)+(1)/(27) )(1)/(64)+cdots , isCAT 2023 Slot 3 · Quant · Sequences and Series
• Q21Let a_n=46+8n and b_n=98+4n be two sequences for natural numbers n≤ 100 . Then, the sum of all terms common to both…CAT 2023 Slot 3 · Quant · Sequences and Series
• Q18For any natural number n , suppose the sum of the first n terms of an arithmetic progression is ( n+2n² ) . If the…CAT 2022 Slot 1 · Quant · Sequences and Series
• Q7On day one, there are 100 particles in a laboratory experiment. On day n , where n≥ 2 , one out of every n particles…CAT 2022 Slot 2 · Quant · Sequences and Series
• Q19Consider the arithmetic progression 3,7,11,ldots and let A_n denote the sum of the first n terms of this progression.…CAT 2022 Slot 2 · Quant · Sequences and Series
• Q17The average of all 3-digit terms in the arithmetic progression 38, 55, 72, ..., isCAT 2022 Slot 3 · Quant · Sequences and Series
• Q14If x_0=1 , x_1=2 and x_n+2=(1+x_n+1)/(x_n) for n=0,1,2,3,ldots , then x_2021 is equal toCAT 2021 Slot 1 · Quant · Sequences and Series
• Q22The natural numbers are divided into groups as (1), (2, 3, 4), (5, 6, 7, 8, 9), ... and so on. Then, the sum of the…CAT 2021 Slot 1 · Quant · Sequences and Series
• Q10Three positive integers x , y and z are in arithmetic progression. If y-x>2 and xyz=5 ( x+y+z ) , then z-x equalsCAT 2021 Slot 2 · Quant · Sequences and Series
• Q20For a sequence of real numbers x_1,x_2,ldots ,x_n , if x_1-x_2+x_3-cdots + ( -1 )^(n+1)x_n=n²+2n for all natural…CAT 2021 Slot 2 · Quant · Sequences and Series
• Q16Consider a sequence of real numbers x_1,x_2,x_3,ldots such that x_n+1=x_n+n-1 for all n≥ 1 . If x_1=-1 then x_100 equalsCAT 2021 Slot 3 · Quant · Sequences and Series