JEE Advanced Mathematics: Sequences & Series Practice Questions

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

Q1.
$Find the sum of the first 20 terms of an arithmetic progression whose first term is 5 and common difference is 3.$
Easy
Q2.
$Find the sum of the infinite geometric series 1, 1/2, 1/4, ...$
Easy
Q3.
$I f t h es u m o f n t er m so f a se q u e n ce i s n^{2}, f in d t h e 5 t h t er m .$
Easy
Q4.
$What is the 10th term of the geometric progression 2, 6, 18, ...?$
Easy
Q5.
$The sum of the series 1 + 2/3 + 4/9 + 8/27 + ... to infinity is:$
Medium
Q6.
$I f t h es u m o f t h e f i r s t n t er m so f ana r i t hm e t i c p r o g r ess i o ni s g i v e nb y S_{n} = 3 n^{2} + 5 n, t h e n t h eco mm o n d i f f er e n ce i s :$
Medium
Q7.
$L e t a se q u e n ce b e d e f in e d b y a_{1} = 1 an d a_{n + 1} = a_{n} + 2 n + 1 f or n >= 1. F in d t h e v a l u eo f a_{100} .$
Medium
Q8.
$If the sum of an infinite geometric series is 3 and the sum of the squares of its terms is 9/2, find the first term.$
Medium
Q9.
$L e t x_{1}, x_{2}, ..., x_{n} b e p os i t i v er e a l n u mb er ss u c h t ha tt h e i r p r o d u c t i s 1. T h e minim u m v a l u eo f (1 + x_{1}) (1 + x_{2}) ... (1 + x_{n}) i s :$
Hard
Q10.
$I f t h es u m o f t h e f i r s t n t er m so f ana r i t hm e t i c p r o g r ess i o ni s S_{n} an d S_{2 n} = 3 S_{n}, t h e n t h er a t i o S_{3 n} / S_{n} i se q u a l t o :$
Hard
Q11.
$The sum of the infinite series 1/1*2*3 + 1/2*3*4 + 1/3*4*5 + ... is:$
Hard
Q12.
$If a, b, care in harmonic progression, then the value of (a+b)/(a-b) + (c+b)/(c-b) is:$
Hard

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