Find the number of terms in an even number series if sum is 240.(show me the simplest way plz).
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hi friend,
2,4,6,8,10,...........is the even number series which is in arithmetic progression whose first term is 2 and common difference is 2
→sum of n terms of an A.p =n/2(2a+(n-1)d)
240=n/2(4+(n-1)2)
480=n(4+2n-2)
480=n(2n+2)
240=n²+n
→n²+n-240=0
→n²+16n-15n-240=0
→n(n+16)-15(n+16)=0
→(n-15)(n+16)=0
n can't be negative ..so number of terms are 15
I hope this will help u ;)
2,4,6,8,10,...........is the even number series which is in arithmetic progression whose first term is 2 and common difference is 2
→sum of n terms of an A.p =n/2(2a+(n-1)d)
240=n/2(4+(n-1)2)
480=n(4+2n-2)
480=n(2n+2)
240=n²+n
→n²+n-240=0
→n²+16n-15n-240=0
→n(n+16)-15(n+16)=0
→(n-15)(n+16)=0
n can't be negative ..so number of terms are 15
I hope this will help u ;)
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