Question

an arithmetic sequence has the the terms t(1) = 9 and t(4) = 24.write the equation for the sequence.hint : find the constant difference (slope), then use it to find term 0.t(n) =

Explanation:

Step1: Find constant difference $d$

Recall arithmetic sequence formula $t(n) = t(1) + (n-1)d$. Substitute $t(1)=9$, $t(4)=24$, $n=4$:
$$24 = 9 + (4-1)d$$
$$24 - 9 = 3d$$
$$15 = 3d$$
$$d = \frac{15}{3} = 5$$

Step2: Find $t(0)$ (term 0)

Use $t(0) = t(1) - d$:
$$t(0) = 9 - 5 = 4$$

Step3: Write sequence equation

General form: $t(n) = t(0) + nd$. Substitute $t(0)=4$, $d=5$:
$$t(n) = 4 + 5n$$

Answer:

Equation for the sequence: $\boldsymbol{t(n) = 5n + 4}$
Term 0: $\boldsymbol{4}$