Question

the recursive formula, and the three terms in the sequence after + d a_1 = ____ 24) 24, -76, -176, -276, ...

Explanation:

Step1: Identify the first - term

The first term $a_1$ of a sequence is the first number in the sequence. Given the sequence $24, - 76, - 176, - 276,\cdots$, $a_1 = 24$.

Step2: Find the common difference $d$

The common difference $d$ of an arithmetic sequence is found by subtracting the first term from the second term. $d=-76 - 24=-100$.

Step3: Find the recursive formula

The recursive formula for an arithmetic sequence is $a_n=a_{n - 1}+d$. Substituting $d = - 100$, we get $a_n=a_{n - 1}-100$ with $a_1 = 24$.

Step4: Find the next three terms

To find the next term after $-276$, we use the formula $a_n=a_{n - 1}+d$.
The next term $a_5=-276+( - 100)=-376$.
The term after that $a_6=-376+( - 100)=-476$.
The term after that $a_7=-476+( - 100)=-576$.

Answer:

The first - term $a_1 = 24$, the recursive formula is $a_n=a_{n - 1}-100$ ($a_1 = 24$), and the three terms after $-276$ are $-376,-476,-576$.