Question

check whether 50 is a term of the arithmetic sequence 2, 5,8... if yes what is the position of the tetm ?

Answer 1

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Answer 2

Yes, 50 is a term of AP and 50 is 17th term of the sequence

Given:

50 is a one of term in a Arithmetic sequence 2, 5,8...  

To find

If 50 is in given AP then position of 50 in AP

Solution:

Given sequence is  2, 5,8...  

Here, first term a = 2,

common difference = term 2 - term 1 = 5 - 2 = 3

⇒ a = 2 and d = 3

As we know nth term of AP, $a_{n}$ = a + (n-1)d  

Let 50 be the nth term then

=>  a + (n-1)d = 50

=>  2 +(n-1)3 = 50   [ ∵ a = 2 and d = 3 ]

=>  3n - 3 = 48

=>  3n = 51

=>  n = 17  

Here, n value is a positive integer, thus 50 exist in given Arithmetic sequence

Therefore, 50 is a term of AP and 50 is 17th term of the sequence

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