Find 𝑎, 𝑏, and 𝑐 given the arithmetic sequence 𝑎, 44, 𝑏, 64, 𝑐.
In an arithmetic sequence, the difference between one term and the next is a constant. If we think about it in terms of a number line, the distance between every value is constant. How do we get from 44 to 64? We add 20.
But that is two spaces in the sequence. And that means that each space in the sequence is plus 10. The sequence increases by 10 units every time. Value 𝑏 would be 10 units more than 44. 𝑏 equals 54. Value 𝑐 is 10 units more than 64, which is 74. And value 𝑎 is 10 units less than 44, 34.
In this sequence, 𝑎 equals 34, 𝑏 equals 54, and 𝑐 equals 74.