find the next three terms in each sequence
1. 3/4, 1 1/2, 2 1/4, 3,...
2. -7, -14, -21, -28,...
Ms. Sue can you help me
for the first, you are adding 3/4 to a term to get the next one
for the second , you are subtracting 7 from a term to get the next one.
To find the next three terms in each sequence, we need to identify the pattern and apply it to determine the subsequent terms.
1. Sequence: 3/4, 1 1/2, 2 1/4, 3,...
The pattern in this sequence can be observed by multiplying each term by a factor of 3/2.
Let's calculate the next three terms:
- The fourth term can be obtained by multiplying the third term, 2 1/4, by 3/2:
2 1/4 * 3/2 = 9/2 = 4 1/2.
So, the fourth term is 4 1/2.
- The fifth term can be found by multiplying the fourth term, 4 1/2, by 3/2:
4 1/2 * 3/2 = 27/4 = 6 3/4.
Hence, the fifth term is 6 3/4.
- Finally, the sixth term can be calculated by multiplying the fifth term, 6 3/4, by 3/2:
6 3/4 * 3/2 = 81/8 = 10 1/8.
Therefore, the next three terms in this sequence are 4 1/2, 6 3/4, and 10 1/8.
2. Sequence: -7, -14, -21, -28,...
In this sequence, each term is obtained by subtracting 7 from the previous term.
Let's determine the next three terms:
- To find the fourth term, subtract 7 from the third term, -21:
-21 - 7 = -28.
Hence, the fourth term is -28.
- The fifth term can be obtained by subtracting 7 from the fourth term, -28:
-28 - 7 = -35.
Thus, the fifth term is -35.
- Finally, to calculate the sixth term, subtract 7 from the fifth term, -35:
-35 - 7 = -42.
Therefore, the next three terms in this sequence are -28, -35, and -42.