Arithmetic Help?

Question

The third term of an arithmetic sequence is 58 and the sixth term is 139. 2 marks.
a) What is the common difference?

b) What is the first term?

Answer 1

a1, a2, 58, a4, a5, 139

The difference of the 6th and 3rd terms is 139 - 58 = 81.
And 81 has to cover the span of 3 terms. So divide by 3.

81/3 = 27

That means the common difference is 27.

Working backwards and forwards:
31 - 27 = 4
58 - 27 = 31
58 - 0 = 58
58 + 27 = 85
85 + 27 = 112
112 + 27 = 139

So the sequence is 4, 31, 48, 85, 112, 139

The first term is 4.

Answer 2

58 + x + x + x = 139
3x = 139 - 58 = 81
x = 81/3 = 27

The common difference is 27

First term is 58 - 27 - 27 = 58 -54 = 4