Question

Help please.
with the steps
on image.
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Answer 1

• T(n) = 3n² - 4
• -189 doesn't belong

Explanation:

Given sequence:

• -1, 8, 23, 44, 71

The first differences:

• 9, 15, 21, 27

The second differences:

• 6, 6, 6

If the sequence is T(n) = an² + bn + c, we have:

• 2a = 6 ⇒ a = 3

Using the first and second differences work out the value of zero term:

• 9 - 6 = 3
• -1 - 3 = -4

This gives us c = - 4

Now we have:

• T(n) = 3n² + bn - 4

The first term is T(1) = -1, substitute n = 1 and find the value of b:

• 3(1²) + b*1 - 4 = - 1
• 3 + b - 4 = - 1
• b = 0

The nth term is:

• T(n) = 3n² - 4

Now lets find if -189 belongs to this sequence:

• - 189 = 3n² - 4
• 3n² = - 185

The left side is positive and the right side is negative so the answer is also negative