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If logea,logeb,logec are in an A.P. and logea-loge2b,loge2b-loge3c,loge3c-logea are also in an A.P., then a:b:c is equal to

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Important Questions on Sequences and Series

MEDIUM
The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is
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If nC4, nC5 and nC6 are in A.P., then n can be
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,,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
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 :
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 :
MEDIUM
If the sum of the first n terms of the series 3+ 75+ 243+ 507+ is 4353, then n equals:
HARD
Let AP a;d denote the set of all the terms of an infinite arithmetic progression with first term a and common difference d>0. If AP1;3AP2;5AP3;7=APa;d then a+d equals ____
HARD
For any three positive real numbers a, b and c. If 925a2+b2+25c2-3ac=15b3a+c. Then
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 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 :
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
The number of terms common to the two A.P.’s 3,7,11,,407 and 2,9,16,,709 is ____________.
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 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
The sum of all natural numbers n such that 100<n<200 and H.C.F. 91,n>1 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
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
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 :
HARD
Let X be the set consisting of the first 2018 terms of the arithmetic progression 1,6,11, , and Y be the set consisting of the first 2018 terms of the arithmetic progression 9,16,23,  . Then, the number of elements in the set XY is___.