Bissoy.com
Doctors Medicines MCQs Q&A

If 3rd, 8th and 13th terms of a GP are p, q and r respectively, then which one of the following is correct?

If 3rd, 8th and 13th terms of a GP are p, q and r respectively, then which one of the following is correct? Correct Answer q<sup>2</sup> = pr

Concept:

If a is the first term and r is the common ratio of a GP then the nth term of GP is given by: an = arn - 1

Calculation:

Given: 3rd, 8th and 13th terms of a GP are p, q and r respectively.

Let a is the first term and R is the common ratio.

⇒ a3 = aR2 = p     ---(1)

⇒ a8 = aR7 = q    ----(2)

⇒ a13 = aR12 = r     ---(3)

Dividing (2) by (1), we get

⇒ q / p = R5          ---(4)

Similarly, by dividing (3) by (2), we get

⇒ r / q = R5          ---(5)

From (4) and (5), we get

⇒ q2 = p × r

Related Questions

A, B, C, D, E, and F are sitting around a circular facing towards the center. They have their birthdays on 2nd, 3rd, 4th, 5th, 6th and 8th. The person born on the 3rd date sits opposite to the person born on 5th. The person born on 3rd does not sit adjacent to E. E sits third to the right of F and was born on 2nd. C sits to the right of E. F was born on the square number date. A sits opposite to C, who was born on the date of the cube number. D sits to the immediate left of E. Who sits exactly between E and B?
Six students of a school – Radha, Raj, Rahul, Mira, Aarav and Arijit are selected from different classes – 7th, 8th, 9th, 10th, 11th and 12th standards (not necessarily in the same order) to perform individually in the school annual function. Their order of performances is decided as per their classes. The one who is in 12th class will perform first, then after that 11th class student will perform and so on. Mira will perform immediate after the Rahul but before Arijit. Mira does not study in 8th class. Raj will perform immediate after Aarav but Raj neither studies in 8th class nor in 7th class. Who will perform last in the school annual function?
There are three classes 7th, 8th, and 9th. If the difference between the average marks of class 7th, 8th and 8th, 9th is 90, then what will be the difference of marks between class 7th and 9th?
Find the sum of 11 terms of an arithmetic progression whose 3rd and 8th terms are -1 and 19 respectively.
If it is possible to make a meaningful word with the 2nd, the 3rd  and the 8th  letters of the word ‘ABSOLUTE’, then which of the following will be the 3rd letter from the left of that word? If more than one such word can be formed give ‘X’ as the answer and if no such word can be formed give ‘Y’ as the answer.
If it is possible to make only one six-letter meaningful English word with the 2nd, 3rd,  and 8th letter of the word FLOCCULANT and 1st, 3rd, and 5th letter of the word GONDOLA, which of the following will be the second letter from the left of that word? If no such word can be made give ‘X’ as the answer and if more than one such word can be made give ‘Y’ as the answer.
If it is possible to make only one six-letter meaningful English word with the 3rd, 6th and 8th letter of the word CANDELABRUM and 3rd, 5th and 7th letter of the word GOSHAWK, which of the following will be the fourth letter from the left of that word? If no such word can be made give ‘X’ as the answer and if more than one such word can be made give ‘Y’ as the answer.
An electronics shop was selling articles at a high discount. Kajal went to buy 3 articles from the shop. The cost of the first article is 33.33% less than the cost of the 2nd article. The cost of the 3rd article is 300% more than the discount on the 2nd article. The discount on the 1st article is 30% less than the discount on the 3rd article. After the discounts, Kajal receives an additional discount, which is equal to the sum of discounts on the first 2 articles. The discount on the 1st article is 80.55% less than the price of the 3rd article. Which of the following is true if the cost of article 1 is 50% less than the cost of article 3?
45% players played in 1st world cup out of which 25 players played in only 1st world cup. 57.5% players played in 2nd world cup out of which 45 players played in only 2nd world cup. 72.5% players played in 3rd world cup out of which 110 players played in only 3rd world cup. Find the players who played in both 1st world cup and 2nd world cup but not in 3rd world cup, if total number of players is 400.
Three alarms are ringed on an interval. If the time interval between 1st and 2nd alarm is 220 secs, 2nd and 3rd alarm is 180 secs and time interval between 3rd and 1st alarm is 88.88% of 2nd and 3rd alarm. After how much time does they ringed together?