Question

In the arithmetic progression 27,24,21 sum of how many terms will be 132 and give reason.
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Answer 1

Answer:

a1 = 27 , a2 = 24

a2 - a1 = d

24 - 27 = -3

Sn = n/2 [2a + (n-1)d]

132 = n/2 [2×27 + (n-1)×-3]

132 = n/2 [ 54 -3n +3]

132 = n/2 [57 - 3n]

132×2 = n[57 - 3n]

264 = 57n - 3n²

57n - 3n² - 264 = 0

-3n² + 57n - 264 = 0

Multiplying by -1

3n² - 57n + 264 = 0

Dividing by 3

n² - 19n + 88 = 0

a + b = -19

a × b = 88

-11 + -8 = -19

-11 × -8 = 88

n² - 19n + 88 = 0

n² - 11n - 8n + 88 = 0

n(n - 11) -8 (n - 11) = 0

(n - 8) (n -11) =0

n = 8 or n = 11

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