Question

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?

Polynomial arithmetic
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?

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: $$a^{60} = a_1 - 4(60 - 1)$$
$$a^{60} = 67 - 4 \cdot 59$$
$$d^{60} = 169$$