The Palmers and the Reynolds are saving money for a trip to Utah to go snowboarding. The Arnolds are going to save a nickel on the first day of the mo

The Reynolds save $0.05 on the first day, and then double the amount in their savings each day after that. Since the amount in their savings is increasing by a constant factor of 2, then the amount in their savings is represented by a geometric sequence with a constant ratio of r= 2 and first term of $a_1=0.05$.
The recursive formula for a geometic sequence is $a_n=r\times a_{n-1}$. We know that r= 2 so the recursive formula for the Reynolds is $a_1=0.05$, $a_n=2a_{n-1}$.
The explicit formula for a geometric sequence is $a_n=a_1{r}^{n-1}$. We know $a_1=0.05$ and r= 2 so the explicit formula for the Reynolds is then $a_n=0.05(2{)}^{n-1}$.
The Palmers save $10 on the first day, and then add $10 more dollars each day after that. Since the amount in their savings in increasing by a constant amount of 10, then the amount in their savings is represented by an arithmetic sequence with a common difference of d=10 and a first term of $a_1=10$.
The recursive formula forarithmetic sequence is $a_n=a_{n-1}+d$. We know d=10 so the recursive formula for Palmers is then $a_1=10$, $a_n=a_{n-1}+10$
The explicit formula for an arithmetic sequence is $a_n=a_1+(n-1)d$. We know $a_1=10$ and d=10 so the explicit formula for the Palmers is then $a_n=10+(n-1)(10)$