3) How many terms of the AP 16,14, 12. are needed to give the sum 60
answers
explain why do we do get two
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ANSWER :
n = 5 or n = 12 is the answer
EXPLANATION :
a = 16, d = - 2, Sn = 60
Sn = n/2 (2a + (n-1)d)
60 = n/2 (2×16 + (n-1)-2)
120 = n(32 - 2n +2)
120 = 34n - 2n²
2n² - 34n + 120 = 0
n² - 17n + 60 = 0.......... (1)
n² - 12n - 5n +60 = 0
n(n-12) - 5(n-12) = 0
n-5 = 0 or n-12 = 0
n = 5 or n = 12
We get two answers because equation (1) is a quadratic equation so it will have 2 roots
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