Question

1. Check whether the following sequences are in A. P.
(i) a–3, a–5, a–7, ...​

Answer 1

Answer:

(i) a – 3, a – 5, a – 7… t2 – t1 = a – 5 – (a – 3) = a – 5 – a + 3 = -2 t3 – t2 = a – 7 – (a – 5) = a – 7 – a + 5 = -2 t2 – t1 = t3 – t2 (common difference is same) The sequence is in A.P. t2 – t1 = 1/3 – 1/2 = (2 - 3)/6 = -1/6 t3 – t2 = 1/4 – 1/3 = (3 - 4)/12 = -1/12 t2 – t1 ≠ t3 – t2 The sequence is not in A.P. (ii) t2 – t1 = 13 – 9 = 4 t3 – t2 = 17 – 13 = 4 t4 – t3 = 21 – 17 = 4 t5 – t4 = 25 – 21 = 4 Common difference are equal ∴ The sequence is in A.P. (iv) t2 – t1 = 0 – (- 1/3) = 0 + 1/3 = 1/3 t3 – t2 = 1/3 – 0 = 1/3 t2 – t1 = t3 – t1 The sequence is in A.P. (v) t2 – t1 = -1 – 1 = -2 t3 – t2 = 1 – (-1) = 1 + 1 = 2 t4 – t3 = -1-(1) = – 1 – 1 = – 2 t5 – t4 = 1 – (-1) = 1 + 1 = 2 Common difference are not equalRead more on Sarthaks.com - https://www.sarthaks.com/935413/check-whether-the-following-sequences-are-in-a-p-i-a-3-a-5-a-7-ii-1-2-1-3-1-4-1-5-iii-9-13-17-21-25