Which term of the sequence given by an = n2 + 2n + 1, n element of N, is 361 ?
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Answer:
a18 = 361
That is the 18th term of sequence n² + 2n + 1 is 361
Step-by-step explanation:
Since we given that
nth term of sequence = an = n² + 2n + 1
And we have to find the values of n for which an = 361
So according to given condition
n² + 2n + 1 = 361 for some n ∈ N where N is set of natural numbers
⇒ n² + 2n + 1 = 361
⇒ n² + 2n - 360 = 0
⇒ n² + 20n - 18n - 360 = 0
⇒ n(n + 20) - 18(n - 20) = 0
⇒ ( n + 20 )( n - 18 ) = 0
⇒ n + 20 = 0 OR n - 18 = 0
⇒ n = -20 OR n = 18
Since
n ∈ N so n ≠ -20 so n = 18
Thus
a18 = 361
That is the 18th term of sequence n² + 2n + 1 is 361
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