### An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three terms is 429. Find the AP.

Download Sample Paper of Class 10 here https://www.teachoo.com/cbse/sample-papers/

Last updated at Dec. 21, 2017 by Teachoo

Download Sample Paper of Class 10 here https://www.teachoo.com/cbse/sample-papers/

Transcript

Question 24 An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three terms is 429. Find the AP. Given Number of terms of AP = 37 So, last term will be 37th term Middle most term = ((37 + 1))/2 = 38/2 = 19th term Theory Let AP be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 Here number of terms = 11 Middle term = 6 So, Middle term = ((11 + 1))/2 = 12/2 = 6 So, 19th term is middle most term Thus, 3 middle most terms will be 18th term, 19th term, 20th term 18th term = a18 = a + (18 – 1)d = a + 17d 19th term = a19 = a + (19 – 1)d = a + 18d 20th term = a20 = a + (20 – 1)d = a + 19d Given Sum of 3 middle most terms = 225 (a + 17d) + (a + 18d) + (a + 19d) = 225 (a + a + a) + (17d + 18d + 19d) = 225 3a + 54d = 225 3(a + 18d) = 225 a + 18d = 225/3 a + 18d = 75 Also, Sum of last 3 terms = 429 Last term = an = a37 = a + (37 – 1)d = a + 36d Second Last term = an – 1 = a37 – 1 = a36 = a + (36 – 1)d = a + 35d Third Last term = an – 2 = a37 – 2 = a35 = a + (35 – 1)d = a + 34d Now Sum of last 3 terms = 429 Putting values (a + 36d) + (a + 35d) + (a + 34d) = 429 (a + a + a) + (36d + 35d + 34d) = 429 3a + 105d = 429 3(a + 35d) = 429 a + 35d = 429/3 a + 35d = 143 Thus, our equations are a + 18d = 7 5 …(1) a + 35d = 143 …(2) Doing (2) – (1) (a + 35d) – (a + 18d) = 143 – 75 a – a + 35d – 18d = 143 – 75 17d = 68 d = 68/17 d = 4 From (1) a + 18d = 7 5 Putting d = 4 a + 18 × 4 = 75 a + 72 = 75 a = 75 – 72 a = 3 Thus, a = 3, d = 4 So, AP is 3, 7, 11, 15, 19, …… 147

Paper Summary

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24 You are here

Question 25

Question 26

Question 27

Question 28

Question 29

Question 30

Class 10

Sample Papers, Previous Year Papers and Other Questions

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.