a How are consecutive terms related to each other?
B
b How are consecutive terms related to each other?
A
a t(n)=- 3n+10
B
b t(n)=2000/3 * 3^(n-1)
Practice makes perfect
a Let's pay close attention to how the consecutive terms are related to each other.
We can see that the consecutive terms have a common difference of - 3. We also see that the first term is 7. Therefore, the given sequence is an arithmetic sequence with first term t(1)= 7 and common difference d= - 3. We can write its equation by substituting these values into the general equation for arithmetic sequences.
b Let's pay close attention to how the consecutive terms are related to each other.
We can see that the consecutive terms have a common ratio of 3. Therefore, the given sequence is an geometric sequence with common ratio r= 3.
t( n)= t(1) r^(n-1)
To find the equation for this sequence, we need to find the value of the first term.
We can do it by substituting r=3 and t(2)=2000 in the equation.
The first term of the sequence is 20003. Therefore, the equation for the given sequence can be written as follows.
t( n)= t(1) r^(n-1) ⇓ t( n)= 2000/3 * 3^(n-1)
