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Problems on Arithmetic Progression - Test Questions

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Question 21

Question: (pq)^t^h term and the sum of pq terms.

Answer: Let a = first term, d = common difference

Subtract (ii) from (i)

Question 22

Question:

Answer:

Question 23

Question: The sum of n terms of three APs are S₁,S₂ and S₃. The first term of each is 1 and common differences are 1, 2 and 3 respectively. Prove that S₁ + S₃ = 2S₂.

Answer:

Question 24

Question: The first and the last term of an AP are a and l respectively. If S denotes the sum of terms show that the common

Answer: a = first term, l = last term, S_n = S_|, d = common difference.

Question 25

Question: The ratio of the sums of m and n terms of an AP is
Show that the ratio of m^t^h and n^t^h terms is (2m - 1) : (2n - 1).

Answer:

Question 26

Question: If the sums of the first p, q, r terms of AP are a, b, c respectively prove that

Answer:

Question 27

Question: If a, b, c are in AP, show that (a - c)² = 4(b² - ac).

Answer:

Question 28

Question: If a² + 2bc, b²+ 2ca, c² + 2ab are in AP, show that

Answer:

Question 29

Question: Two cars start together in the same direction at the same place. The first goes with uniform speed of 15 km/hr, the second goes at the speed of 10 km/hr in the first hour and increases the speed by 0.1 km each succeeding hour. After how many hours will the second car over take the first if both cars go non stop?

Answer: Speed of second car = 10 km/hr
Uniform Speed of the first car = 15 km/hr
The second car increases its speed by 1 km every hour.

Since both cars are travelling in the same direction, the distance covered will be same.

They are together initially or after 11 hours. Thus the second car over takes the first car after 11 hours of journey.