Find or investigate the function as requested.
-If t(n) represents the nth term of a sequence for $\mathrm { n } \in \mathrm { N }$ and $t ( n ) = n ^ { 2 } + 2 n + 5$ , then is 29 a value of the function whose domain is N ?
A) No
B) Yes

Question

Find or investigate the function as requested.
-If  t(n)  represents the nth term of a sequence for $\mathrm { n } \in \mathrm { N }$ and $t ( n ) = n ^ { 2 } + 2 n + 5$ , then is 29 a value of the function whose domain is  N ?
A) No
B) Yes

Quizplus · Accepted Answer

To determine if 29 is a value of the function $t(n) = n^2 + 2n + 5$, we substitute 29 for $t(n)$ and solve for $n$: $29 = n^2 + 2n + 5$. Simplifying, we get $n^2 + 2n - 24 = 0$, which factors to $(n+6)(n-4) = 0$. Thus, $n = -6$ or $n = 4$. Since $n$ must be a natural number ($n \in N$), $n = 4$ is the valid solution. Therefore, 29 is indeed a value of the function for $n \in N$.

Find or Investigate the Function as Requested n∈N\mathrm { n } \in \mathrm { N }n∈N

Find or Investigate the Function as Requested $\mathrm { n } \in \mathrm { N }$