Question

Which term of the sequence given by an = n2 + 2n + 1, n element of N, is 361 ?​

Answer 1

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