Question

Is 5,8,11,14,.... an A.P. ? If so then what will be the 100th term? check whether 92 in this A.P. ? Is number 61 in this A.P​

Answer 1

Answer:

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Step-by-step explanation:

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

Answer 2

The 100th term is "302"

92 in this A.P.- " YES"

61 in this A.P.- " NO"

Step-by-step explanation:

5,8,11,14... is a A.P.

1) By using Tn= a + (n-1)d formula we can get the 100th term

here a = starting value.

         n= The number of term

         d= difference between each term.

T100= 5 +(100-1) 3

T100= 5+ 99*3

T100= 5+297

T100=302.

2) 92 is in the A.P.?

We can find out whether it is in the term by subtract the starting value(a)

and then dividing with the difference between each term(d). From this if we get remainder as 0, it is in the A.P.

(92-5)/3= 87/3= 29is quotient and the remainder 0.

92 is in the A.P.

3) 61 is in the A.P.?

(61-5)/3= 56/3=18 is quotient and remainder 2.

61 is not in the A.P.