Question

50 POINTS! The fifth term of an arithmetic sequence is 11 and the tenth term is 41. What is the first term?

Answer 1

The common difference d is

• (41–11) / (10–5) = 6.

The first term is

• 11 - 6(5–1) = -13.

so , the first term is -13

Answer 2

• -13

Explanation:

The fifth term:

• 
  `a_5=a+4d = 11`

The 10th term:

• 
  `a_(10)=a+9d=41`

Subtract side-by-side and find d:

• 9d - 4d = 41 - 11
• 5d = 30
• d = 6

Find the first term:

• a = 11 - 4*6
• a = 11 - 24
• a = - 13