Sequence and Series questions
1035 published questions with worked solutions.
- In an AP, the pth term is q and the (p+q)th term is 0. Then the qth term is
- In a sequence of (4n+1) terms the first (2n+1) terms are in AP whose common difference is 2, and the last (2n+1) terms are in GP...
- If x^2 + 9y^2 + 25z^2 = xyz ( 15 x + 5 y + 3 z ) then x, y, z are in
- The largest term common to the sequences 1, 11, 21, 31, to 100 terms and 31, 36, 41, 46, to 100 terms is
- The interior angles of a convex polygon are in AP, the common difference being 5^ . If the smallest angle is 2 /3 then the number...
- The minimum number of terms of 1 + 3 + 5 + 7 + that add up to a number exceeding 1357 is
- In the sequence 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, , where n consecutive terms have the value n, the 150th term is
- In the sequence 1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, , where n consecutive terms have the value n, the 1025th term is
- Let t_n be a sequence of integers in GP in which t_4 : t_6 = 1 : 4 and t_2 + t_5 = 216. Then t_1 is
- If ( 5c a ), ( 3b 5c ) and ( a 3b ) are in AP, where a, b, c are in GP, then a, b, c are the lengths of sides of
- If the pth, qth and rth terms of an AP are in GP then the common ratio of the GP is
- The number of terms common between the series 1 + 2 + 4 + 8 + to 100 terms and 1 + 4 + 7 + 10 + to 100 terms is
- The 10th common term between the series 3 + 7 + 11 + and 1 + 6 + 11 + is
- Three consecutive terms of a progression are 30, 24, 20. The next term of the progression is
- If three numbers are in GP then the numbers obtained by adding the middle number to each of the three numbers are in
- If a_1, a_2, a_3 are in AP, a_2, a_3, a_4 are in GP and a_3, a_4, a_5 are in HP then a_1, a_3, a_5 are in
- If a, b, c, d are four numbers such that the first three are in AP while the last three are in HP then
- If the first two terms of an HP be 2/5 and 12/23 then the largest positive term of the progression is the
- If x, 2y, 3z are in AP, where the distinct numbers x, y, z are in GP, then the common ratio of the GP is
- If x > 1, y > 1, z > 1 are three numbers in GP then 1 1 + x , 1 1 + y , 1 1 + z are in
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