Question

Check whether 301 is a term of the list of number 5,11,17,23

Answer 1

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=>a = 5

=>d = 6

=>an = 301

an = a +(n - 1)d

301 = 5 +(n -1)6

301 = 5 + 6n -6

301 = -1 + 6n

301 + 1 = 6n

302 = 6n

n = 302/6

This is not a natural number.

Therefore 301 is not a term of the given AP.

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Answer 2

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step-by-step explanation:

Given series,,

5, 11, 17, 23, ..........

It is in A.P

where,

1st term, a = 5

common difference, d = 11-5 = 6

Now,

to find whether 301 is a yerm of this AP,

we take 301 as ${n}^{th}$ term of this AP

Now,

we know that,

${n}^{th}$ term of an AP is given by,

$a_{n}$ = a + (n-1)d

where,

a is 1st term

d is common diffrence

n is any natural number

So,

putting the value,

$a_{n}$ = 301

we get,

=> a +(n-1)d = 301

now,

putting the value of 'a' and 'd' ,

we get,

=> 5 + 6(n-1) = 301

=> 6n - 6 = 296

=> 6n = 296+6

=> 6n = 302

=> n = 302/6

=> n = 151/3

Here,

n is not a natural number

Hence,

301 is not the term of this AP.