Check whether 301 is a term of the list of nu | vedclass

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Question

(B) We have the sequence $5, 11, 17, 23, \ldots$First,we check if it is an Arithmetic Progression $(AP)$:$a_{2}-a_{1} = 11-5 = 6$$a_{3}-a_{2} = 17-11

Vedclass · Accepted Answer

No

Vedclass · Answer

(B) We have the sequence $5, 11, 17, 23, \ldots$First,we check if it is an Arithmetic Progression $(AP)$:$a_{2}-a_{1} = 11-5 = 6$$a_{3}-a_{2} = 17-11 = 6$$a_{4}-a_{3} = 23-17 = 6$Since the common difference $d = 6$ is constant,the sequence is an $AP$ with first term $a = 5$.Let $301$ be the $n$th term of this $AP$. The formula for the $n$th term is:$a_{n} = a + (n-1)d$Substituting the values:$301 = 5 + (n-1)6$$301 = 5 + 6n - 6$$301 = 6n - 1$$302 = 6n$$n = \frac{302}{6} = \frac{151}{3} = 50.33$Since $n$ must be a positive integer for any term in an $AP$,and $50.33$ is not an integer,$301$ is not a term of the given list of numbers.

Check whether $301$ is a term of the list of numbers $5, 11, 17, 23, \ldots$

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