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Sagot :
Answer:
- 9th, 10th and 11th terms; 32, 37 and 42
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Given AP:
- -8, - 3, 2, ...
We observe that:
- The first term is a = - 8,
- The common difference is d = -3 - (-8) = 2 - (-3) = 5.
Let the three terms be aₙ, aₙ₊₁, aₙ₊₂.
Use nth term formula:
- aₙ = a + (n - 1)d = - 8 + (n - 1)*5 = - 8 + 5n - 5 = 5n - 13
The following two terms are:
- aₙ₊₁ = 5n - 13 + 5 = 5n - 8
- aₙ₊₂ = 5n - 8 + 5 = 5n - 3
Their sum is 111, set an equation and solve for n:
- 5n - 13 + 5n - 8 + 5n - 3 = 111
- 15n - 24 = 111
- 15n = 135
- n = 135/15
- n = 9
The three terms are 9th, 10th and 11th terms and they are:
- 5*9 - 13 = 45 - 13 = 32
- 32 + 5 = 37
- 37 + 5 = 42
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