web analytics

Ex 5.2, 16 - Determine the AP whose third term is 16 - Ex 5.2

  1. Chapter 5 Class 10 Arithmetic Progressions
  2. Serial order wise
Ask Download

Transcript

Ex 5.2 ,16 Determine the A.P. whose third term is 16 and the 7th term exceeds the 5th term by 12 We know that an = a + (n – 1) d So, a3 = a + (3 – 1) d a3 = a + 2d 16 = a + 2d a + 2d = 16 Also, a7 = a + (8 – 1)d a7 = a + 6d Similarly, a5 = a + (4 – 1)d a5 = a + 4d Given that 7th term exceeds the 5th term by 12 7th term – 5th term = 12 a7 – a5 = 12 (a + 6d) – (a + 4d) = 12 a + 6d – a – 4d = 12 a – a + 6d – 4d = 12 0 + 6d – 4d = 12 2d = 12 d = 12/2 d = 6 Putting the value of d in (1) a = 16 – 2d = 16 – 2× 6 = 16 – 12 = 4 Hence, First term of AP = a = 4 Second term of AP = first term + common difference = 4 + 6 = 10 Third term of AP = second term + common difference = 10 + 6 = 16 So, the AP is 4, 10, 16,…

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
Jail