List of top Quantitative Ability and Data Interpretation Questions on Sequence and Series

A ball is dropped from a height of 200 meters. After striking the floor it rebounces to \(\frac{4}{5}\)th of the height from where it fell. The total distance it travels before coming to rest is ______
The sum of all two digit numbers that give a remainder 2 when they are divided by 7 is ______
Let \(a\) and \(b\) be the roots of the quadratic equation \(x^2 + 3x - 1 = 0\). If \(P_n = a^n + b^n\) for \(n \geq 0\), then for \(n \geq 2\), \(P_n =\)
The 288th term of the sequence a, b, b, c, c, c, d, d, d, d, ... is:
Questions 43 and 44 are based on the following instructions: each question gives a statement followed by three conclusions, I, II and III. Pick the option that tells you which of the three conclusions can be derived from the statement alone.

Statement: \(A_0, A_1, A_2, \ldots\) is a sequence of numbers with \(A_0 = 1\), \(A_1 = 3\), and \(A_t = (t+1)A_{t-1} - tA_{t-2}\) for \(t = 2, 3, 4, \ldots\)

Conclusion I: \(A_8 = 77\)
Conclusion II: \(A_{10} = 121\)
Conclusion III: \(A_{12} = 145\)
Consider a sequence -6, -12, 48, 24, -30, -36, 42, ... continuing in the same style. If the sum of the first n terms of the sequence is 132, what is the value of n?
For each \(p > 1\), a sequence \(A_n\) is defined by \(A_0 = 1\) and \(A_n = np + (-1)^n A_{n-1}\) for \(n \geq 1\). For how many integer values of \(p\) is 1000 a term of the sequence?
Let \(\{A_n\}\) be a unique sequence of positive integers satisfying the following properties: \(A_1 = 1,\ A_2 = 2,\ A_4 = 12\), and \(A_{n+1}\cdot A_{n-1} = A_n^2 \pm 1\) for \(n = 2, 3, 4, \dots\)
Then, \(A_7\) is:
Directions for questions 49 and 50: Read the information given below and answer the question.
Let \(f\) be a function defined on the set of integers. Assume that \(f\) satisfies the following properties:
1. \(f(0) \neq 0\);
2. \(f(1) = 3\); and
3. \(f(x)f(y) = f(x+y) + f(x-y)\) for all integers \(x\) and \(y\).

What is \(f(3)\)?
Directions for questions 49 and 50: Read the information given below and answer the question.
Let \(f\) be a function defined on the set of integers. Assume that \(f\) satisfies the following properties:
1. \(f(0) \neq 0\);
2. \(f(1) = 3\); and
3. \(f(x)f(y) = f(x+y) + f(x-y)\) for all integers \(x\) and \(y\).

What is \(f(7)\)?