Q58 of 74 Page 9

Insert two numbers between 3 and 81 so that the resulting sequence is G.P.


Let the two numbers between 3 and 81 be G1 and G2.

Thus 3, G1, G2, 81 are in G.P.

Let r be the common ratio.

Therefore ar3 = 81

or 3r3 = 81

or r3 = 27 or r = 3

or G1 = 3 × 3 = 9

G2 = 9 × 3 = 27

Hence the two required numbers are 9 and 27.

More from this chapter

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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.

57
If a, b, c, d are in G.P., show that (a2 + b2 + c2)(b2 + c2 + d2) = (ab + bc + cd)2

59
Find the value of n so that (an+1 + bn+1)/(an + bn) may be the geometric mean between the a and b.

60
The sum of two numbers is 6 times their geometric mean. Show that the numbers are in the ratio  3 + 2 2 : 3 – 22.