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How many terms of the A.P. −6, \[- \frac{11}{2}\], −5, ... are needed to give the sum −25?
Concept: undefined >> undefined
In an A.P. the first term is 2 and the sum of the first five terms is one fourth of the next five terms. Show that 20th term is −112.
Concept: undefined >> undefined
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If S1 be the sum of (2n + 1) terms of an A.P. and S2 be the sum of its odd terms, then prove that: S1 : S2 = (2n + 1) : (n + 1).
Concept: undefined >> undefined
Find an A.P. in which the sum of any number of terms is always three times the squared number of these terms.
Concept: undefined >> undefined
If the sum of n terms of an A.P. is nP + \[\frac{1}{2}\] n (n − 1) Q, where P and Q are constants, find the common difference.
Concept: undefined >> undefined
The sums of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6. Find the ratio of their 18th terms.
Concept: undefined >> undefined
The sums of first n terms of two A.P.'s are in the ratio (7n + 2) : (n + 4). Find the ratio of their 5th terms.
Concept: undefined >> undefined
If \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P., prove that:
\[\frac{b + c}{a}, \frac{c + a}{b}, \frac{a + b}{c}\] are in A.P.
Concept: undefined >> undefined
If \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P., prove that:
a (b +c), b (c + a), c (a +b) are in A.P.
Concept: undefined >> undefined
If a2, b2, c2 are in A.P., prove that \[\frac{a}{b + c}, \frac{b}{c + a}, \frac{c}{a + b}\] are in A.P.
Concept: undefined >> undefined
If a, b, c is in A.P., then show that:
a2 (b + c), b2 (c + a), c2 (a + b) are also in A.P.
Concept: undefined >> undefined
If a, b, c is in A.P., then show that:
b + c − a, c + a − b, a + b − c are in A.P.
Concept: undefined >> undefined
If a, b, c is in A.P., then show that:
bc − a2, ca − b2, ab − c2 are in A.P.
Concept: undefined >> undefined
If \[\frac{b + c}{a}, \frac{c + a}{b}, \frac{a + b}{c}\] are in A.P., prove that:
\[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P.
Concept: undefined >> undefined
If \[\frac{b + c}{a}, \frac{c + a}{b}, \frac{a + b}{c}\] are in A.P., prove that:
bc, ca, ab are in A.P.
Concept: undefined >> undefined
If a, b, c is in A.P., prove that:
(a − c)2 = 4 (a − b) (b − c)
Concept: undefined >> undefined
If a, b, c is in A.P., prove that:
a2 + c2 + 4ac = 2 (ab + bc + ca)
Concept: undefined >> undefined
If a, b, c is in A.P., prove that:
a3 + c3 + 6abc = 8b3.
Concept: undefined >> undefined
If \[a\left( \frac{1}{b} + \frac{1}{c} \right), b\left( \frac{1}{c} + \frac{1}{a} \right), c\left( \frac{1}{a} + \frac{1}{b} \right)\] are in A.P., prove that a, b, c are in A.P.
Concept: undefined >> undefined
Show that x2 + xy + y2, z2 + zx + x2 and y2 + yz + z2 are consecutive terms of an A.P., if x, y and z are in A.P.
Concept: undefined >> undefined
