a Let's take a look at the first few terms in the given sequence to determine the first term and the common difference.
40+20 →60+20 →80We can use this information to write an equation for the nth term of the sequence. Explicit rules for the nth term of an arithmetic sequence follow a certain format.
a_n= a_1+( n-1) d
In this form, a_1 is the first term in the sequence, d is the common difference, and n is the position of the desired term in the sequence. We found that the common difference is d= 20 and the first term a_1= 40. Let's write and simplify the rule.
b This time we want to find the explicit formula of the given geometric sequence. Explicit rules of geometric sequences follow a general format.
a_n= a_1 r^(n-1)
Here, a_1 is the first term in the sequence, d is the common ratio, and n is the position of the desired term in the sequence. Let's start our rule by identifying the first term and calculating the common ratio.
We can now use the common ratio 12 and the first term 3 to write the rule for the sequence.
a_n= 3( 1/2 )^(n-1)
