<img height="1" width="1" style="display:none" src="https://www.facebook.com/tr?id=539359806247306&ev=PageView&noscript=1"/>

Ex 9.2, 3 - In AP, first term is 2, sum of first five terms is - Arithmetic Progression (AP): Formulae based

  1. Chapter 9 Class 11th Sequences and Series
  2. Serial order wise
Ask Download

Transcript

Ex9.2 , 3 In an A.P, the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20th term is –112. It is given that First term = a = 2 Also Sum of first five terms = 1/4 (Sum of next 5 terms) Sum of first five terms = 1/4 (Sum of 6th to 10th terms) Sum of first five terms = 1/4 (■8(█("Sum of first 10 terms " @" – Sum of first five terms" ))) S5 = 1/4(S10 – S5) 4S5 = S10 – S5 4S5 + S5 = S10 5S5 = S10 Finding sum of first five terms We know that Sum of n terms of A.P. = 𝑛/2(2a + (n – 1)d) Sn = 𝑛/2(2a + (n – 1)d) Putting a = 2, n = 5 S5 = 5/2 (2(2) + (5 – 1)d) = 5/2 (4 + 4d) = 5/2 (4) + 5/2 (4)d = 10 + 10d Finding sum of first ten terms Sn = 𝑛/2(2a + (n – 1)d) Putting a = 2, n = 10 S10 = 10/2 (2(2) + (10 – 1)d) = 10/2 (4 + 9d) = 5(4 + 9d) = 20 + 45d From equation (1) 5S5 = S10 Putting values 5(10 + 10d) = 20 + 45d 50 + 50d = 20 + 45d 50d – 45d = 20 – 50 5d = – 30 d = (−30)/5 = – 6 To find 20th term, we use the formula an = a + (n – 1)d where an = nth term , n = number of terms, a = first term , d = common difference Here, a = 2 , d = – 6 , n = 20 Putting values a20 = 2 + (20 – 1) (–6) = 2 + (19)(-6) = 2 – 114 = – 112 Thus, 20th term of sequence is – 112 Hence proved.

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 contact him here.
Jail