Question

Check weather 92 is a different between any 2 terms of the sequence

Answer 1

Answer:

i. The given sequence is 5, 8,11,14,… Here, t1 = 5, t2 = 8, t3 = 11, t4 = 14 ∴ t2 – t1 = 8 – 5 = 3 t3 – t2 = 11 – 8 = 3 t4 – t3 = 14 – 11 = 3 ∴ t2 – t1 = t3 – t2 = t4 – t3 = 3 = d = constant The difference between two consecutive terms is constant ∴ The given sequence is an A.P. ii. tn = a + (n – 1)d ∴ t100 = 5 + (100 – 1)3 …[∵ a = 5, d = 3] = 5 + 99 × 3 = 5 + 297 ∴ t100 = 302 ∴ 100th term of the given A.P. is 302. iii. To check whether 92 is in given A.P., let tn = 92 ∴ tn = a + (n – 1)d ∴ 92 = 5 + (n – 1)3 ∴ 92 = 5 + 3n – 3 ∴ 92 = 2 + 3n ∴ 90 = 3n ∴ n = 90/3 = 30 ∴ 92 is the 30th term of given A.P. iv. To check whether 61 is in given A.P., let tn = 61 61 = 5 + (n – 1)3 ∴ 61 = 5 + 3n – 3 ∴ 61 = 2 + 3n ∴ 61 – 2 = 3n ∴ 59 = 3n ∴ n = 59/3 But, n is natural number 59 ∴ n ≠ 59/3 ∴ 61 is not in given A.P.Read more on Sarthaks.com - https://www.sarthaks.com/845139/is-11-14-an-if-so-then-what-will-be-the-100th-term-check-whether-92-is-in-this-is-number-61-in-this