How many terms of the A.P 9,17,25.. must be taken to get a sum 450?
Please give clear answer with explanation. Please
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Answer:
n = 10
Step-by-step explanation:
Series is 9,17,25...
Sum of n terms = Sn = (n/2)*{2a + (n - 1)d}
In the given problem, a = 9, d = 17 - 9 = 8 and Sn = 450.
Putting the values,
=> 450 =(n/2)*{18 + (n - 1) * 8}
=> 900 = n[18 + 8n - 8]
=> 900 = n[10 + 8n]
=> 900 = 10n + 8n^2
=> 8n^2 + 10n - 900 = 0
=> 8n^2 - 80n+ 90n - 900 = 0
=> 8n(n - 10) + 90(n - 10) = 0
=> (8n - 90)(n - 10) = 0
=> n = 10, n = 11.25{Rejected because it's not a whole number}
Hence, the number of terms = 10.
#Hope my answer help you!
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