The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q2 = ps.
Let a be the first term and r be the common ratio of the G.P.
According to the given condition,
a5 = a r5–1 = a r4 = p … (1)
a8 = a r8–1 = a r7 = q … (2)
a11 = a r11–1 = a r10 = s … (3)
Dividing equation (2) by (1), we obtain
Dividing equation (3) by (2), we obtain
Equating the values of r3 obtained in (4) and (5), we obtain
Thus, the given result is proved.
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.
How many terms of G.P. 3, 32, 33, … are needed to give the sum 120?
Find the sum of all numbers between 200 and 400 which are divisible by 7.
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
Suppose 3 bulbs are selected at random from a lot. Each bulb is tested and classified as defective (D) or non-defective (N). Write the sample space of this experiment?
Find the sum to n terms of the series 3 × 8 + 6 × 11 + 9 × 14 +…
Find the sum of all numbers between 200 and 400 which are divisible by 7.
Find the 20th and nthterms of the G.P.
Find the sum to n terms of the series 1 × 2 × 3 + 2 × 3 × 4 + 3 × 4 × 5 + …
Find four numbers forming a geometric progression in which third term is greater than the first term by 9, and the second term is greater than the 4th by 18.
The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.
For what values of x, the numbers are in G.P?
The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.
If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are .
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