Sequence and Series questions
1035 published questions with worked solutions.
- A GP consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying odd places, then...
- The sum of the series 1 3 7 + 1 7 11 + 1 11 15 + is
- Statement 1: If sum of n terms of a series is 6n^2+3n+1 then the series is in AP. Statement 2: Sum of n terms of an AP is always...
- Let a_n be n^ th term of the GP of positive numbers. Let _ n=1 ^ 100 a_ 2n = and _ n=1 ^ 100 a_ 2n-1 = , such that , then the...
- If the sides of a right angled triangle are in AP, then the sides are proportional to
- Let the sequence a_1,a_2,a_3, ,a_ 2n form an AP, then a_1^2-a_2^2+a_3^2- -a_ 2n ^2 is equal to
- If a,b,c be in GP, then a^n, b^n, c^n will be
- 150 workers were engaged to finish a piece of work in a certain number of days. 4 workers dropped the second day, 4 more workers...
- Consider the following statements: 1+3+5+ upto n terms =n^2 (Statement 1); 2+4+6+ upto n terms =n^2+1 (Statement 2). Which of the...
- The GM of roots of the equation x^2-18x+9=0 is
- If the sum of two extreme numbers of an AP with four terms is 8 and product of remaining two middle terms is 15, then greatest...
- If _ax, _bx, _cx be in HP, then a,b,c are in
- If m is a root of the given equation (1-ab)x^2- (a^2+b^2 )x-(1+ab)=0 and m harmonic means are inserted between a and b, then the...
- The number which should be added to the numbers 2,14,62, so that the resulting numbers may be in GP, is
- If 9 AM's and HM's are inserted between 2 and 3 and if the harmonic mean H is corresponding to arithmetic mean A, then A+ 6H is...
- Statement 1: Let F_1(n)=1+ 12+ 13+ + 1n, then _ r=1 ^nF_1(r)=(n+1)F_1(n)-n. Statement 2: 1^ -1 +2^ -1 +3^ -1 + +n^ -1 n> ( 1+2+3+...
- If m^ th term of HP is n and n^ th term is m, then the r^ th term will be
- If a^ n+1 +b^ n+1 a^n+b^n be the harmonic mean between a and b, then the value of n is
- If 1 b-c , 1 c-a , 1 a-b be consecutive terms of an AP, then (b-c)^2,(c-a)^2,(a-b)^2 will be in
- If a_1=a_2=2, a_n=a_ n-1 -1 (n>2), then a_5 is
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