Question

note: please make sure to properly format your answers. all dollar figures in the answers need to include the dollar sign and comma ($2,354.67). all percentage values in the answers need to include a percentage sign (%). for all items without specific rou
find the missing terms indicated by variables in the arithmetic sequence shown. a, 30, b, 42, c, d, e

Explanation:

Step1: Find the common difference

The common difference $d$ of an arithmetic sequence can be found using two known terms. Given the terms $30$ and $42$, and since in an arithmetic - sequence $a_{n}=a_{1}+(n - 1)d$, and if we assume $a_{2}=30$ and $a_{4}=42$. Then $a_{4}-a_{2}=(a_{1}+3d)-(a_{1}+d)=2d$. So, $2d = 42 - 30=12$, and $d=\frac{42 - 30}{2}=6$.

Step2: Find the value of $a$

Since $a$ is the first - term and $30$ is the second - term, and $a_{2}=a + d$. Then $a=a_{2}-d=30 - 6 = 24$.

Step3: Find the value of $b$

Since $b$ is the third - term, $b=a_{2}+d=30 + 6 = 36$.

Step4: Find the value of $c$

Since $c$ is the fifth - term, $c=a_{4}+d=42 + 6 = 48$.

Step5: Find the value of $d$

Since $d$ is the sixth - term, $d=a_{5}+d=48 + 6 = 54$.

Step6: Find the value of $e$

Since $e$ is the seventh - term, $e=a_{6}+d=54 + 6 = 60$.

Answer:

a. $24$
b. $36$
c. $48$
d. $54$
e. $60$