Question
Answer the Following Questions:
It is known that the 8th term of an arithmetic sequence is 12 and the 10th term is 67. Determine:
a.) Is the first term
b.) The difference
c.) 𝑈18
<Answer>
How It Works:
From the information given, we can make two equations:
1.3rd term (𝑈3 = 12):
𝑈3 = 𝑎 + (3 − 1)𝑏 → 𝑎 + 2𝑏 = 12 (𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 1)
2.10th term (𝑈10 = 67):
𝑈10 = 𝑎 + (10 − 1)𝑏 → 𝑎 + 9𝑏 = 67 (𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 2)
a.First Term
55
To find the first term, we use the method of substituting the value 𝑏= into Equation 1
7
(because it is simpler).
Answer the Following Questions:
It is known that the 8th term of an arithmetic sequence is 12 and the 10th term is 67. Determine:
a.) Is the first term
b.) The difference
c.) 𝑈18
<Answer>
How It Works:
From the information given, we can make two equations:
1.3rd term (𝑈3 = 12):
𝑈3 = 𝑎 + (3 − 1)𝑏 → 𝑎 + 2𝑏 = 12 (𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 1)
2.10th term (𝑈10 = 67):
𝑈10 = 𝑎 + (10 − 1)𝑏 → 𝑎 + 9𝑏 = 67 (𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 2)
a.First Term
55
To find the first term, we use the method of substituting the value 𝑏= into Equation 1
7
(because it is simpler).
