A Christmas tree is decorated with bulbs such that first branch has 5 bulbs, 7 in the second, 9 in the third and so on. If the tree is to have a total of 525 bulbs on it, how many branches must be used in his design?
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Answer:
21 branches
Step-by-step explanation:
Given : d = 7-5= 2 , a= 5
Sn = 525
Substitute the above in the formula
Sn = n/2 (2a + (n-1)d)
525 = n/2 (2*5 + (n-1) 2)
525 = n/2 (10+2n-2)
525= n/2 (8+2n)
525*2=8n+2n²
1050= 8n +2n²
n²+4n-525
n²+25n -21n -525
n(n+25) -21(n+25)
(n+25)(n-21)
n= -25,21
since the number of branches cannot be in negative, we take n= 21
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