Problems on Arithmetic Series

Question 11

Question:  
in AP.

Answer:   

Question 12

Question:   Show that if the positive numbers a,b,c are in AP, so are the

Answer:    Since a,b,c are in an AP, we have



Now, we shall show that sum of extreme terms is double the middle terms.

Question 13

Question:   Find the sum of the following series:
i. 8 + 21 + 34 +---- to n terms

Answer:    i. 8 + 21 + 34 +---- to n terms

Question 14

Question:   Find the sum of the series

Answer:   

Question 15

Question:   Find the sum of 32 terms of an AP whose 3^rd term is 1 and 6^th term is -11.

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


Solving for a and d, we have a = 9, d = -4

Question 16

Question:   Find the sum to first hundred even natural numbers divisible by 5.

Answer:    S = 10 + 20 + 30 + 40 +-----to 100 terms

Question 17

Question:   The sum of 3^rdand 7^th term of an AP is 42 and the sum of the 7^th and the 11^th term of same AP is 82. Find the first term and the common difference.

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

Question 18

Question:   If a₁, a₂, a₃, a₄----a_n are in AP prove that

Answer:   

Question 19

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

Answer:   

Question 20

Question:  
are in AP.

Answer:    (b - c)², (c - a)², (a - b)²are in AP, then