The first term of a geometric sequence is –2 and the common ratio is -1/-4. What are the next three terms of the sequence?
2 answers:
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Answer: x = 3, y = 1, z = 2
<u>Step-by-step explanation:</u>
EQ 1: x - y - z = 0
EQ 3:<u> -x + 2y + z = 1 </u>
y = 1
EQ 2: 2x - 3y + 2z = 7 → 1(2x - 3y + 2z = 7) → 2x - 3y + 2z = 7
EQ 3: -x + 2y + z = 1 → -2( -x + 2y + z = 1) → <u>-2x + 4y + 2z = 2</u>
y + 4z = 9
y = 1 ⇒ 1 + 4z = 9
4z = 8
z = 2
Input y = 1 and z = 2 into one of the equations to solve for x:
EQ 1: x - y - z = 0
x - (1) - (2) = 0
x - 3 = 0
x = 3
Check:
EQ 2: 2x - 3y + 2z = 7
2(3) - 3(1) + 2(2) = 7
6 - 3 + 4 = 7
3 + 4 = 7
7 = 7