Question:
how many terms of the A.P 9,17,25... Must be taken to give a sum of 636.main sirf ye kehna chahta hu ki is sum mein n/2 ka lcm liya means uski two numbers ke saath cutting kar di but aur kisi sum mein esa nahi kahi.why? please help me
Answer:
Given AP is:
9, 17, 25,...........
where the first term a = 9
common difference d = 17 - 9 = 8
Let l is the last term and n is the total number of terms in the AP
Sum = 636
=> (n/2)(a + l) = 636
=> n(9 + l) = 636*2
=> n(9 + l) = 1272 ............1
Again l = a + (n-1)d
=> l = 9 + (n-1)8
=> l = 9 + 8n - 8
=> l = 8n + 1 ..........2
Put value of l in equation 1, we get
n(9 + 8n + 1) = 1272
=> n(8n + 10) = 1272
=> 8n2 + 10n - 1272 = 0
=> 4n2 + 5n - 636 = 0 (divide by 2)
=> (n - 12)*(4n + 53) = 0
=> n = 12, -53/12
Since n can not be negative
So n = 12 i.e. number of terms is 12
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