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The sum of three numbers which are consecutive terms of an A.P. is 21. If the second number is reduced by 1 and the third is increased by 1, we obtain three consecutive terms of a G.P. Find the numbers.
Concept: undefined >> undefined
The sum of three numbers a, b, c in A.P. is 18. If a and b are each increased by 4 and c is increased by 36, the new numbers form a G.P. Find a, b, c.
Concept: undefined >> undefined
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The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an A.P. Find the numbers.
Concept: undefined >> undefined
If a, b, c are in G.P., prove that:
a (b2 + c2) = c (a2 + b2)
Concept: undefined >> undefined
If a, b, c are in G.P., prove that:
\[a^2 b^2 c^2 \left( \frac{1}{a^3} + \frac{1}{b^3} + \frac{1}{c^3} \right) = a^3 + b^3 + c^3\]
Concept: undefined >> undefined
If a, b, c are in G.P., prove that:
\[\frac{(a + b + c )^2}{a^2 + b^2 + c^2} = \frac{a + b + c}{a - b + c}\]
Concept: undefined >> undefined
If a, b, c are in G.P., prove that:
\[\frac{1}{a^2 - b^2} + \frac{1}{b^2} = \frac{1}{b^2 - c^2}\]
Concept: undefined >> undefined
If a, b, c are in G.P., prove that:
(a + 2b + 2c) (a − 2b + 2c) = a2 + 4c2.
Concept: undefined >> undefined
If a, b, c, d are in G.P., prove that:
\[\frac{ab - cd}{b^2 - c^2} = \frac{a + c}{b}\]
Concept: undefined >> undefined
If a, b, c, d are in G.P., prove that:
(a + b + c + d)2 = (a + b)2 + 2 (b + c)2 + (c + d)2
Concept: undefined >> undefined
If a, b, c, d are in G.P., prove that:
(b + c) (b + d) = (c + a) (c + d)
Concept: undefined >> undefined
If a, b, c are in G.P., prove that the following is also in G.P.:
a2, b2, c2
Concept: undefined >> undefined
State the converse and contrapositive of statement:
If it is hot outside, then you feel thirsty.
Concept: undefined >> undefined
State the converse and contrapositive of statement:
I go to a beach whenever it is a sunny day.
Concept: undefined >> undefined
State the converse and contrapositive of statement:
A positive integer is prime only if it has no divisors other than 1 and itself.
Concept: undefined >> undefined
State the converse and contrapositive of statement:
If you live in Delhi, then you have winter clothes.
Concept: undefined >> undefined
State the converse and contrapositive of statement:
If a quadrilateral is a parallelogram, then its diagonals bisect each other.
Concept: undefined >> undefined
If a, b, c are in G.P., prove that the following is also in G.P.:
a3, b3, c3
Concept: undefined >> undefined
Rewrite of the statement in the form "p if and only if q".
p : If you watch television, then your mind is free and if your mind is free, then you watch television.
Concept: undefined >> undefined
Rewrite of the statement in the form "p if and only if q".
q : If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.
Concept: undefined >> undefined
