How many terms of the ap 16 14 12
Asked by admin @ in Math viewed by 348 People
How many terms of the A.P 16, 14, 12 are needed to give the sum 60? Explain why we get two answers
Answered by admin @
Answer:
Step-by-step explanation:
16 , 14 , 12 ,...............
a=16 , d = -2 , Sn = 60 , n=?
Sn= n/2 [2a+(n-1)d]
60 = n/2[2×16 +(n-1)-2]
60×2=n [32-2n +2]
120= n (34 -2n)
120=34n -2n²
2n²-34n+120=0
÷2
n²-17n + 60=0
(60n²=-20n & +3n)
n²-20n+3n + 60
n(n-20)-3(n-20)
(n-20) or (n-3)
n-20=0 or n-3 =0
.:. n = 20 or n = 3
Its has 2 solutions because sum of 60 will comes till 20 terms or till 3 terms.
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