Consider the sequence 67, 63, 59, 55...... a. show that the sequence is arithmetic. b. find a formula for the general term Un. c. Find the 60th term of the sequence. d. Is -143 a member of the sequence? e. Is 85 a member of the sequence?

Question
Polynomial arithmetic
asked 2020-10-18
Consider the sequence \(67, 63, 59, 55......\) a. show that the sequence is arithmetic. b. find a formula for the general term Un. c. Find the 60th term of the sequence. d. Is -143 a member of the sequence? e. Is 85 a member of the sequence?

Answers (1)

2020-10-19
Step 1 Consider the given series: \(67, 63, 59, 53...\) Step 2 The terms of the series can be denoted as follows: \(a_1 = 67,\)
\(a_2 = 63,\)
\(a_3 = 59,\)
\(a_4 = 55,\) Step 3 Now check the type of the series: \(a_1 - a_2 = 67 - 63 = 4,\)
\(a_2 - a_3 = 63 - 59 = 4,\)
\(a_3 - a_4 = 59 - 55 = 4,\) Since \(a_1 - a_2 = a_2 - a_3 = a_3 - a_4 = 4,\) Therefore series is arithmetic Step 4 The formula for the nth term is determined as follows: \(a_1 = 67,\)
\(a_2 = 63,\)
\(a_2 = a_1 - 4 \cdot (2-1),\)
\(a_3 = 59,\)
\(a_3 = a_1 -4(3-1),\) Now determine thr \(6^(th)\) term sa follows: \(a^{60} = a_1 - 4(60 - 1)\)
\(a^{60} = 67 - 4 \cdot 59\)
\(d^{60} = 169\)
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