How many terms of the A.P. 16, 14, 12,.. are needed to give the sum 60? Explain
why do we get two answers.
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Answer:
AP = 16 , 14 , 12 , .
a = 16
- d = 14-16 = (-2)
- Sum = 60
Sum of n terms = n/2{2a + (n-1)d}
- 60 = n/2{2(16) + (n-1)(-2)}
- 60 = n/2{ 32-2n+2}
- 60x2 = n(34-2n)
- 120 = 34n -2n²
- 2n² - 34n + 120 = 0
- 2(n²-16n+60) = 0
- n² - 16n + 60 = 0
- n² - 6n - 10n + 60 = 0
- n(n-6) - 10(n-6) = 0
- (n-10) (n-6) = 0
Answer :- n = 6 or n = 10
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