Breakup G Strategy | AP , GP + Equation | Moderate
In an arithmetic progression, if the sum of fourth, seventh and tenth term is 99, and the sum of the first fourteen terms is 497, then the sum of first five terms is : [TITA]
CAT Progressions questions (2023–2025) — actual Quant questions with solutions
11 real CAT Progressions questions from CAT 2023 to CAT 2025, each with options, the verified answer and a step-by-step solution. Practice one topic at a time,
11 real CAT questions · CAT 2023–2025 · 2 Medium
Shruti travels a distance of 224 km in four parts for a total travel time of 3 hours. Her speeds in these four parts follow an arithmetic progression, and the corresponding time taken to cover these four parts follow another arithmetic progression. If she travels at a speed of 960 meters per minute for 30 minutes to cover the first part, then the distance, in meters, she travels in the fourth part is
Consider the sequence: \[ t_1 = 1, \quad t_2 = -1, \quad t_n = \left( \frac{n - 3}{n - 1} \right)t_{n - 2} \quad \text{for } n \geq 3. \] Find the value of the sum: \[ \frac{1}{t_2} + \frac{1}{t_4} + \frac{1}{t_6} + \cdots + \frac{1}{t_{2022}} + \frac{1}{t_{2024}}. \]
Algebra + APGP + Fractions
Infinite Series Solution Find the sum of the series \[ \frac{1}{5} \left( \frac{1}{5} - \frac{1}{7} \right) + \left( \frac{1}{5} \right)^2 \left( \left( \frac{1}{5} \right)^2 - \left( \frac{1}{7} \right)^2 \right) + \left( \frac{1}{5} \right)^3 \left( \left( \frac{1}{5} \right)^3 - \left( \frac{1}{7} \right)^3 \right) + \cdots \]
Find the sum of the series \[ \frac{1}{5} \left( \frac{1}{5} - \frac{1}{7} \right) + \left( \frac{1}{5} \right)^2 \left( \left( \frac{1}{5} \right)^2 - \left( \frac{1}{7} \right)^2 \right) + \left( \frac{1}{5} \right)^3 \left( \left( \frac{1}{5} \right)^3 - \left( \frac{1}{7} \right)^3 \right) + \cdots \]
Suppose \( x_1, x_2, x_3, \ldots, x_{100} \) are in an arithmetic progression such that \( x_5 = -4 \) and \( 2x_6 + 2x_9 = x_{11} + x_{13} \). Then, \( x_{100} \) equals
Find the sum of the infinite series: (1/5)(1/5 − 1/7) + (1/5)²((1/5)² − (1/7)²) + …
Given a sequence defined as t1 = 1, t2 = −1, and tn = (n−3)/(n−1) × tn−2 for n ≥ 3. Find the value of 1/t2 + 1/t4 + 1/t6 + … + 1/t2024.
Suppose X1, X2, X3, . . . , X100 are in arithmetic progression such that X5 = −4 and 2X6 + 2X9 = X11 + X13. Then, X100 equals
Let \( a_n = 46 + 8n \) and \( b_n = 98 + 4n \) be two sequences. Find the sum of all terms common to both sequences.
Amal, Sunil, and Kamal can individually complete a job in a certain number of days, forming a harmonic progression. Kamal takes twice as much time as Amal to do the same amount of work. If Amal and Sunil work for 4 and 9 days respectively, and Kamal needs to work for 16 days to finish the remaining job, then the number of days Sunil will take to finish the job working alone is:
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