Question

3, 8, 13 is an arithmetic sequence .Will the difference between any two terms of the sequence be 60 why check whether 116 is a term of the sequence ​

Answer 1

it is given that, 3, 8 , 13 is an arithmetic sequence .

here first term, a = 3

and common difference , d = 13 - 8 = 8 - 3 = 5

so, nth term = a + (n - 1)d = 3 + (n - 1)5....(1)

question asked “ will the difference between any two terms of the sequence be 60”

answer : of course, yes!

as we can see common difference of sequence is 5 which is a prime factor of 60.

if we choose two random terms within sequence, i.e., first term and nth term

nth term - first term = 60

or, 3 + (n - 1)5 - 3 = 60

or, n = 13

hence, difference between 13th term and first term will be 60.

it means, difference between (m + 12)th term and mth term of the given sequence is 60.

now, 116 is a term of sequence ?

116 = Tn = 3 + (n - 1)5

or, 113 = (n - 1)5

or, 113/5 = n - 1

or, n = 118/5 ≠ integer

so, 116 is not a term of given sequence.

Answer 2

Answer:

it is given that, 3, 8 , 13 is an arithmetic sequence .

here first term, a = 3

and common difference , d = 13 - 8 = 8 - 3 = 5

so, nth term = a + (n - 1)d = 3 + (n - 1)5....(1)

question asked “ will the difference between any two terms of the sequence be 60”

answer : of course, yes!

as we can see common difference of sequence is 5 which is a prime factor of 60.

if we choose two random terms within sequence, i.e., first term and nth term

nth term - first term = 60

or, 3 + (n - 1)5 - 3 = 60

or, n = 13

hence, difference between 13th term and first term will be 60.

it means, difference between (m + 12)th term and mth term of the given sequence is 60.

now, 116 is a term of sequence ?

116 = Tn = 3 + (n - 1)5

or, 113 = (n - 1)5

or, 113/5 = n - 1

or, n = 118/5 ≠ integer

so, 116 is not a term of given sequence.