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

Answer:

• -13

Step-by-step 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