Bissoy.com
Doctors Medicines MCQs Q&A

In an arithmetic progression (AP), the 9th term is 5 times the 2nd term and the 8th term is 1 more than 10 times the first term. What is the 4th term of the geometric progression (GP) whose first term is the second term of AP and whose common ratio is equal to the common difference of AP?

In an arithmetic progression (AP), the 9th term is 5 times the 2nd term and the 8th term is 1 more than 10 times the first term. What is the 4th term of the geometric progression (GP) whose first term is the second term of AP and whose common ratio is equal to the common difference of AP? Correct Answer 448

Given:

The 9th term is 5 times the 2nd term and the 8th term is 1 more than 10 times the first term. 

Formula used:

an = a + (n - 1)d

GP(geometric progression) nth term number 

Tn = ar(n - 1)

Where, a = first term, an = last term, d = common difference in AP, r = Common ratio in GP, Tn = n th term of GP 

Calculation:

The first term of AP is 'a' and common difference is 'd'

The 9th term is 5 times the 2nd term

⇒ 9th term = 5 times 2nd term

⇒ a + 8d = 5(a + d)

⇒ 3d = 4a

⇒ d = 4a/3      ----(1)

8th term is 1 more than 10 times the first term

⇒ a + 7d = 10 a + 1

⇒ 7d = 9a + 1     ----(2)

Putting the value of d in equation 2

⇒ 7(4a/3) = 9a + 1

⇒ a = 3

Putting value of 'a' in equation (1)

⇒ d = 4 × 3/3

⇒ d = 4

According to the question, 

Second term of AP = First time of GP 

⇒ 3 + 4 = 7

Common ratio of GP = 4

Tn = ar(n - 1)

⇒ T(4) = 7 × 4(4 - 1)

⇒ T(4) = 7 × 64 

⇒ 448

∴ The fourth term of GP is 448.

Related Questions

The following question has three statements. Study the question and the statements and decide which of the statement (s) is/are necessary to answer the question. What is the first term of the arithmetic progression? I) The difference between the 16th term and 9th term of an arithmetic progression is 49. II) The average of 12 terms of an arithmetic progression is 40.5. III) The common difference is 5 more than the first term of the arithmetic progression.
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?
In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity I: A sum of 45 terms of an Arithmetic progression is 5400. The ratio between the 11th term and 51st term is 3 : 13. Find the difference between the first term of progression and the common difference between the terms of progression. Quantity II: What should come to the place of ‘?’ in the following question: 234 + 35% of 920 – 4 / 5th of 110 = 7 / 9th of 378 + ? × 87
The sum to infinity of a geometric progression is 39/2. The sum to infinity to squares of the terms of the geometric progression is 253.5. What is the sum to infinity of cubes of the terms of the geometric progression?
The average of ten numbers is 72. The average of the first four numbers is 69 and that of the next three numbers is 74. The 8th number is 6 more than the 9th number and 12 more than the 10th number. What is the average of the 8th and 9th numbers?
$$\frac{{38 \times 38 \times 38 + 34 \times 34 \times 34 + 28 \times 28 \times 28 - 38 \times 34 \times 84}}{{38 \times 38 + 34 \times 34 + 28 \times 28 - 38 \times 34 - 34 \times 28 - 38 \times 28}}$$            is equal to = ?
Simplify the value of $$\frac{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} \times {\text{0}}{\text{.3}} - {\text{3}} \times 0.9 \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}}}}{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} - 0.9 \times {\text{0}}{\text{.2}} - {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}} - 0.3 \times 0.9}} = ?$$
The average of 12 numbers is 25.5. The average of the first six numbers is 22.4 and that of the last three numbers is 28.2. The 7th number is 5 less than the  8th  number but 10 less than the 9th number. What is the average of the 8th and 9th numbers?
If 3rd term of a geometric progression is 1/9 and common multiple is 1/3, then what is the sum of first four terms of the geometric progression?
“What is the different between height and radius of solid cylinder?” Which of the following option is sufficient alone to find the answer? A) A solid cylinder is made by melting a solid sphere. The radius of cylinder is 3 times the radius of a circle whose area is 154 sq.m. Height of cylinder is equal to the height of cone whose volume is 2772 cubic meters. B) Area of a rectangle whose longer side is ¾ times the radius of a solid cylinder, is 168 sq.m and, Volume of solid cylinder is 2772 cubic meters and its height is 18 m. C) A metallic cone of radius 15m and height 35m is melted into the solid cylinder of radius equal to the radius of a circle whose area is equal to the area of rectangle whose sides are in the ratio 4 : 3 respectively. D) The curved surface area of the solid cylinder is 3 time the surface area of a sphere of radius 7m and height of cylinder is equal to the height of a metallic cone whose curved surface area is 308 sq.m.