Question

In the pattern 2,4,6,8... all the numbers are increasing by 2. In the pattern 5,10,15,20,... all the numbers are increasing by 5. In the pattern 12,a,b,35,c... All the numbers are increasing by the same number as well. Determine what the value of c is based off this pattern

Answer 1

Answer: 42 2/3

Step-by-step explanation:

In arithmetic sequences, each term increases by a constant amount. In the terms 12, a, b, and 35, the constant is added 3 times to get to 35. so:
12 + 3C = 35
3C = 23
C = 23/3, or 7 2/3
Now, you can add C to get the next term after 35:
35 + 7 2/3 = 42 2/3

Sequence:
12, 19 2/3, 27 1/3, 35, 42 2/3