Exercise 68 Page 269

To find the explicit equation for this sequence, let's start by seeing how the sequence is changing from term to term. Each term is obtained by adding $5$ to the previous one, with the first term being $t(1)=3.$ We see that $t(2)$ is obtained by adding $5$ to $3$ one time, and $t(3)$ is obtained by adding $5$ to $3$ two times. Therefore, $t(n)$ can be obtained by adding $5$ to $4$ $n-1$ times. This leads us to the explicit formula $t(n)=3+5(n-1).$

To find the explicit equation for this sequence, let's start by seeing how the sequence is changing from term to term. Each term is obtained by subtracting $5$ to the previous one, with the first term being $t(1)=24.$ We see that $t(2)$ is obtained by subtracting $5$ from $24$ one time, and $t(3)$ is obtained by subtracting $5$ from $24$ two times. Therefore, $t(n)$ can be obtained by subtracting $5$ from $24$ $n-1$ times. This leads us to the explicit formula $t(n)=24-5(n-1).$

To find the explicit equation for this sequence, let's start by seeing how the sequence is changing from term to term. Each term is obtained by adding $2.5$ to the previous one, with the first term being $t(1)=7.$ We see that $t(2)$ is obtained by adding $2.5$ to $7$ one time, and $t(3)$ is obtained by adding $2.5$ to $7$ two times. Therefore, $t(n)$ can be obtained by adding $2.5$ to $7$ $n-1$ times. This leads us to the explicit formula $t(n)=7+2.5(n-1).$