Arithmetic Progression- Test Questions

Question 11

Question:   Find three numbers in AP whose sum is 24 and whose product is 440.

Answer:    Let a-d, a, a+d be three numbers in AP
Then (a - d) + (a) + (a + d) = 24
3a = 24
a = 8
(a - d)(a)(a + d) = 440
(8 - d)(8)(8 + d) = 440

Question 12

Question:   Find three numbers in AP whose sum is 9 and sum of their cubes is 153.

Answer:    Let a-d, a, a+d be three numbers in AP.

Question 13

Question:   Find the four numbers in AP whose sum is -4 and the product is 105.

Answer:   










The numbers are

Question 14

Question:   If a, b, c are in AP, then prove that a²(b + c), b²(c + a), c²(a + b) are in AP.

Answer:   

Question 15

Question:  

Answer:   

Question 16

Question:   Find the sum of the following series:

Answer:   



Note that we can find n directly by using the formula for an A.P.





= 15(7 + 145) = 15 x 152 = 2280

Question 17

Question:   If S_n = 3n² + 4n denotes the sum of n terms of a progression, Prove that it is an AP. Find the r^th term.

Answer:   




(This is independent of n). Hence the progression is an AP.

Question 18

Question:   If S_n = 2n² + 3n denote the sum of a progression, prove that it is an AP. Find (2n)^thterm.

Answer:   


d is independent of n. The progression is an AP.

Question 19

Question:   The sum of certain numbers in AP is 5500. If the first and the last terms are 100 and 1000 respectively, find the number of terms.

Answer:   

Question 20

Question:   If the first term of an AP is 2 and the sum of first five terms is equal to one fourth of the sum of next five terms, then show that
i) t₂₀ = -112
ii) find the sum of the first 40 terms.

Answer:    a = first term, d = common difference




S₁₀ - S₅ = 10 + 35d
But (10 + 35d) = 4S₅