For a series whose nth term is , the sum of r terms is :
15th term of the A.P., x – 7, x – 2, x + 3,.... is
[Sol^{n}: a_{n} = a + (n  1)× d
where d = x – 2  x + 7 = 5, a = x  7
⇒a_{15} =(x  7) + (15  1) ×5 = (x  7) + 14 ×5
⇒a_{15} = x  7 + 70 = x + 63]
The sum of first 24 terms of an A.P. a_{1}, a_{2}, a_{3},...; if it is known that a_{1} + a_{5} + a_{10} + a_{15} + a_{20} + a_{24} = 225, is equal to :
A student read common difference of an AP is – 2 instead of 2 and got the sum of first five terms as – 5. The actual sum of first five terms is :
The sum of n terms of two A.P's are in the ratio of (7n + 1) : (4n + 27). The ratio of their 11th terms is –
If 1^{2} + 2^{2} + 3^{2} + ..... n^{2} = 1015, then the value of n is :
The sum of the series + ... upto 9 terms is :
The sum of first n odd natural numbers is :
If the roots of the equation x^{3} – 12x^{2} + 39x – 28 = 0 are in A.P., then their common difference will be :
If A.M between two numbers is 5 and their G.M. is 4, then their H.M. is :
If A is the single A.M. between two numbers a and b and S is the sum of n A.M.'s between them, then S/A depends upon :
If the A.M. between the roots of a quadratic equation is 8 and the G.M. is 5, then the equation is :
If c is the harmonic mean between a and b, then is equal to :
If a,b,c,d,e,f are in A.P. then e–c is equal to :
20th term of the series : + ......... is :
If the value of 1^{3} + 2^{3} + 3^{3} + ...+n^{3} = 2025, then the value of 1 + 2 + 3 +...+ n is :
If the value of 1 + 2 + 3 +... + n is 55, then the value of 1^{3} + 2^{3} + 3^{3} + .... + n^{3} is :
The nth term of the series 1 + +............... is :
1^{2} + 1 + 2^{2} + 2 + 3^{2} + 3 + ... + n^{2} + n is equal to :
The next term of the sequence (1/4,1/36,1/144) ............ is :
If the sum of first n natural numbers is onefifth of the sum of their squares, then n equals :
The nth term of the series 1 + 3 + 6 + 10 + 15 + ... is :
The sum of the series 1^{2} + 1 + 2^{2} + 2 + 3^{2} + 3 + ... + up to n terms is :
The nth term of the sequence
The sum of n terms of the series (1^{2} – 2^{2}) + (3^{2 }– 4^{2}) + (5^{2} – 6^{2}) +... is :
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