Prev

Next

Q54 of 74 Page 9

If the p^th, q^th and r^th terms of a G.P. are a, b, c respectively, prove that a^q-r . b^r-p . c^p-q = 1.

Let x be the first term and R the common ratio.

T_p = x R^p-1 = a ………(1)

T_q = x R^q-1 = b ……….(2)

T_r = x R^r-1 = c ………(3)

a^q-r =

=

...........(1)

b^r-p =

………….(2)

c^p-q =

……….(3)

L.H.S. = (1) x (2) x (3)

.

=1.

More from this chapter

52

Show that the products of the corresponding, terms of the sequences a, ar, ar², ….ar^{n – 1} and A, AR, AR²,……AR^{n – 1} form a G.P. and find the common ratio.

53

Find four numbers forming a Geometric progression in which the third term is greater than the first by 9, and the second term is greater than the fourth by 18.

55

If the first and the n^th terms of a G.P are a and b respectively and if p is the product of the first n terms, prove that P² = (ab)ⁿ.

56

Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n+1)th to (2n)th term is 1/rⁿ.