JEE Main Mathematics: Sequences & Series Practice Questions

15 questions with answers and step-by-step solutions. Tap any question to see the full worked solution.

Q1.
$Find the 10th term of the arithmetic progression 2, 5, 8, 11, ...$
Easy
Q2.
$Find the arithmetic mean of 4 and 16.$
Easy
Q3.
$What is the common ratio of the geometric progression 3, 6, 12, 24, ...?$
Easy
Q4.
$What is the sum of the first 10 terms of the geometric progression 1, 2, 4, 8, ...?$
Easy
Q5.
$Which term of the sequence 5, 8, 11, 14, ... is 32?$
Easy
Q6.
$If the sum of the first 10 terms of an arithmetic progression is 155 and the sum of the first 20 terms is 610, then the sum of the first 30 terms is:$
Medium
Q7.
$The value of the sum 1*2*3 + 2*3*4 + 3*4*5 + ... + n(n+1)(n+2) is:$
Medium
Q8.
$I f t h es u m o f t h e f i r s t n t er m so f a ser i es i s 2 n^{2} + 5 n, t h e n t h e 10 t h t er m o f t h eser i es i s :$
Medium
Q9.
$If a, b, care in geometric progression and a, x, b are in arithmetic progression, and b, y, care in arithmetic progression, then 1/x + 1/y equals:$
Medium
Q10.
$If the sum of an infinite geometric series is 3 and the sum of the squares of its terms is 9/2, then the first term of the series is:$
Medium
Q11.
$If a, b, care in harmonic progression, then the value of (a-b/b-c) is equal to?$
Hard
Q12.
$I f t h es u m o f t h e f i r s t n t er m so f ana r i t hm e t i c p r o g r ess i o ni s S n, an d S_{2} n = 3 * S n, t h e n f in d t h er a t i o S_{3} n / S n .$
Hard
Q13.
$Let a sequence be defined by a1 = 1 and an+1 = an + 1/an for n >= 1. Find the integer part of a100.$
Hard
Q14.
$L e t x b e t h es u m o f t h eser i es 1 + 2 r + 3 r^{2} + ... t o in f ini t y, w h er e ∣ r ∣ < 1. I f x = 9/4, f in d r .$
Hard
Q15.
$Find the sum of the infinite series 1/1*2*3 + 1/2*3*4 + 1/3*4*5 + ...$
Hard

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