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Question
Decide whether 301 is term of given sequence 5, 11, 17, 23,.....
Activity :- Here, d = `square`, therefore this sequence is an A.P.
a = 5, d = `square`
Let nth term of this A.P. be 301.
tn = a + (n – 1) `square`
301 = 5 + (n – 1) × `square`
301 = 6n – 1
n = `302/6` = `square`
But n is not positive integer.
Therefore, 301 is `square` the term of sequence 5, 11, 17, 23,......
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Solution
Here, d = 11 – 5 = \[\boxed{6}\], therefore this sequence is an A.P.
a = 5, d = \[\boxed{6}\]
Let nth term of this A.P. be 301.
tn = a + (n – 1) \[\boxed{\text{d}}\]
∴ 301 = 5 + (n – 1) × \[\boxed{6}\]
∴ 301 = 5 + 6n – 6
∴ 301 = 6n – 1
∴ 6n = 302
∴ n = `302/6` = \[\boxed{\frac{151}{3}}\]
But n is not positive integer.
Therefore, 301 is \[\boxed{\text{not}}\] the term of sequence 5, 11, 17, 23,......
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