Progressions and series covers arithmetic, geometric, and harmonic progressions and series, AGP, sum of series, special series, and AM-GM inequality. Solve the practice questions and go through the detailed explanations and video solutions to learn this topic.

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Instructions

For the following questions answer them individually

Question 1

There are 8436 steel balls stacked in a pile with one ball on the top, 3 balls in the second layer, 6 balls in the third layer, 10 balls in 4th layer and so on. Find the total number of layers.

Question 2

A sequence is such that in any set of four consecutive terms, the sum of first and third term is equal to the sum of second and fourth term. If the third term is equal to 5, 26th term is equal to 9 and the sum of first 18 terms is equal to 58, find the first term.

Question 3

From the first 25 natural numbers, how many arithmetic progressions of 6 terms can be formed such that common difference of the AP is a factor of the 6th term.

Question 4

The ratio of the 8th and 17th terms of an AP is 5:11. The product of the first and the sixth terms of the AP is 176. If the AP has only negative terms in the series, find the sum of the first 200 terms of the series.

Question 5

A bouncing ball loses just 25% of its energy on impact with the ground. If the ball is dropped from a height of 30m, find the total distance travelled by the ball before it comes to rest. Neglect air resistance.

Question 6

Find the sum of the infinite terms of the series 2/3, 7/18, 23/108, 73/648 and so on till infinity

Question 7

Find the arithmetic mean of 842321 and 456661 ?

Question 8

Find the sum of the series 82, 113, 144, … ,609 ?

Question 9

Find the sum of first 99991 odd numbers?

Question 10

Find the harmonic mean between 8 and 56 ?

Question 11

If a,b,c are in A.P and $$a^2,b^2 ,c^2$$ are in H.P and $$a\ne\ b\ne\ c$$ then which of the following is true ?

Question 12

There are 8436 steel balls stacked in a pile with one ball on the top, 3 balls in the second layer, 6 balls in the third layer, 10 balls in 4th layer and so on. Find the total number of layers.

Question 13

The sides of a right angled triangle are in Geometric Progression. What is the ratio of cos of the acute angles of the triangle ?

Question 14

The first term of a GP is positive and the 70th term of the GP is greater that the 69th term. If the first, third and twenty-seventh terms of an AP are equal to the first, second and fourth terms of this GP, what is the ratio of the twenty-fifth term of the AP to the seventh term of the GP?

Question 15

If 12, 20 are geometric mean and Arithmetic mean between two numbers then find the Harmonic mean between them ?

Question 16

Find the sum of first 6 terms of series 19683, 6561, 2187 …?

Question 17

Find the sum of 8000 + 6400+ 5120 + 4096 +….

Question 18

Find the sum of first 10 terms of series 4 ,12, 36 …

Question 19

The ratio of sum till nth terms of two arithmetic progressions is $$\frac{6+n}{2}$$.Find the ratio of the 10th term of both the AP's.

Question 20

If 2x + y = 28, then find the maximum value of $$x^4y^3$$.

Question 21

Find the sum of the following series: 1 + 2 + 5 + 10 + 17 + 26....till 50 terms.

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