Question

Is 302 a term of the A.P. 3,8,13 ?
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Answer 1

Answer:

where 'a' is the first term and 'd' is the common difference. If the value of 'n' is a whole number then 302 will be a term of the S.P. ... and if 'n' is a fraction then302 will not be a term of the A.P.

Step-by-step explanation:

Here, we have been provided with an A.P. having terms 3, 8, 13, We have to check whether 302 will be a term of the A.P. or not.

Now, let us denote the first term of the A.P. with ‘a’, common difference with ‘d’ and 

nthnth

 term with 

TnTn

. On observing the above A.P we can say that: - 

⇒a=3⇒d=T2−T1=8−3=5⇒a=3⇒d=T2−T1=8−3=5

So, let us assume that 302 is the 

nthnth

 term of the A.P. denoted with 

TnTn

. So, we have,

⇒Tn=302⇒Tn=302

Now, we know that the 

nthnth

 term of an A.P. is given by the relation: - 

Tn=a+(n−1)dTn=a+(n−1)d

. So, we have,

⇒a+(n−1)d=302⇒a+(n−1)d=302

 - (1)