GATE · Engineering Mathematics

Sequences and series

28 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 28 questions

The first term of an arithmetic progression is $7$ and its common difference is $4$ . What is the sum of its first $9$ terms?
The first term of an arithmetic progression is $5$ and its common difference is $4$ . What is the sum of its first $20$ terms?
The first term of an arithmetic progression is $8$ and its common difference is $6$ . What is the sum of its first $17$ terms?
The first term of an arithmetic progression is $5$ and its common difference is $5$ . What is the sum of its first $18$ terms?
The first term of an arithmetic progression is $2$ and its common difference is $2$ . What is the sum of its first $14$ terms?
The first term of an arithmetic progression is $5$ and its common difference is $5$ . What is the sum of its first $19$ terms?
What is the sum to infinity of the geometric series $2 + 1/2 + 1/8 + \dots$ ?
The first term of an arithmetic progression is $5$ and its common difference is $5$ . What is the sum of its first $15$ terms?
The first term of an arithmetic progression is $9$ and its common difference is $6$ . What is the sum of its first $11$ terms?
The first term of an arithmetic progression is $6$ and its common difference is $6$ . What is the sum of its first $17$ terms?
The first term of an arithmetic progression is $3$ and its common difference is $6$ . What is the sum of its first $12$ terms?
The first term of an arithmetic progression is $4$ and its common difference is $5$ . What is the sum of its first $12$ terms?
The first term of an arithmetic progression is $8$ and its common difference is $5$ . What is the sum of its first $10$ terms?
What is the sum to infinity of the geometric series $6 + 4 + 8/3 + \dots$ ?
What is the sum to infinity of the geometric series $3 + 3/2 + 3/4 + \dots$ ?
What is the sum to infinity of the geometric series $12 + 3 + 3/4 + \dots$ ?
What is the sum to infinity of the geometric series $12 + 4 + 4/3 + \dots$ ?
What is the sum to infinity of the geometric series $6 + 3 + 3/2 + \dots$ ?
What is the sum to infinity of the geometric series $12 + 6 + 3 + \dots$ ?
What is the sum to infinity of the geometric series $2 + 4/3 + 8/9 + \dots$ ?
What is the sum to infinity of the geometric series $8 + 8/3 + 8/9 + \dots$ ?
What is the sum to infinity of the geometric series $8 + 2 + 1/2 + \dots$ ?
What is the general solution of the second-order homogeneous differential equation d^2y/dx^2 - 6 dy/dx + 9y = 0?
What is the particular integral of the differential equation d^2y/dx^2 + 4y = sin(2x)?
What is the integrating factor of the first-order linear differential equation (dy/dx) + (2/x) y = x^3?
By the ratio test, what is the radius of convergence R of the power series ∑_(n=1 to ∞) [(3^n) / n^2] * (x - 2)^n?
For the Cauchy-Euler differential equation x^2 (d^2y/dx^2) - 2x (dy/dx) + 2y = 0 for x > 0, what is the general solution?
What is the sum of the infinite geometric series S = 3/4 + 3/16 + 3/64 + 3/256 + ...?

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