MEDIUM
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The number of common terms in the progressions 4,9,14,19,, up to 25th  term and 3,6,9,12 up to 37th  term is :

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Important Questions on Sequences and Series

MEDIUM
If x, y, z are positive numbers in A.P. and tan-1xtan-1y and  tan-1z are also in A.P., then which of the following is correct.
MEDIUM
If the sum of the first n terms of the series 3+ 75+ 243+ 507+ is 4353, then n equals:
HARD
The number of terms in an A.P. is even, the sum of the odd terms in it is 24 and that the even terms is 30. If the last term exceeds the first term by 1012, then the number of terms in the A.P. is 
MEDIUM
Let a1, a2, a3,an, ,be in A.P. If a3+a7+a11+a15=72, then the sum of its first 17 terms is equal to :
HARD
For any three positive real numbers a, b and c. If 925a2+b2+25c2-3ac=15b3a+c. Then
MEDIUM
Let a1, a2, a3,,a49 be in A.P. such that Σ k = 0 1 2 a4k+1=416 and a9+a43=66. If a12+a22++a172=140m, then m is equal to:
MEDIUM
If a1/x=b1/y=c1/z and a,b,c are in geometrical progression, then x,y,z are in
MEDIUM
Let a1, a2, a3... be an A.P. with a6=2. Then, the common difference of this A.P., which maximise the product a1·a4·a5,is :
HARD
If nC4, nC5 and nC6 are in A.P., then n can be
HARD
The houses on one side of a road are numbered using consecutive even numbers. The sum of the numbers of all the houses in that row is 170. If there are at least 6 houses in that row and a is the number of the sixth house, then
MEDIUM
Let the sum of the first n terms of a non-constant A.P., a1, a2, a3, ...., an be 50n+n(n-7)2A, where A is a constant. If d is the common difference of this A.P., then the ordered pair d, a50 is equal to
HARD
Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178. If the first term of this A.P. is 10, then the median of the A.P. is :
MEDIUM
If the sum and product of the first three terms in an A.P. are 33 and 1155, respectively, then a value of its 11th term is:
HARD
Given an A.P. whose terms are all positive integers. The sum of its first nine terms is greater than 200 and less than 220.  If the second term in it is 12, then its 4th term is :
HARD
The sum of all natural numbers n such that 100<n<200 and H.C.F. 91,n>1 is
MEDIUM
If a1,a2,a3,.... are in A.P. such that a1+a7+a16=40, then the sum of the first 15 terms of this A.P is
EASY
Let Sn denote the sum of the first n terms of an A.P.. If S4=16 and S6=-48 , then S10 is equal to:
HARD
Let a, b, c, d, e be natural numbers in an arithmetic progression such that a+b+c+d+e is the cube of an integer and b+c+d is a square of an integer. The least possible value of the number of digits of c is
MEDIUM
Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the common ratio of the G.P. is :
MEDIUM
The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is