A.P.
Algebra
Level
2
All terms of an Arithmetic Progression are natural numbers. The sum of its first nine terms lies between 200 and 220. If the second term is 12, then first term is
The answer is 8.
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1 solution
Let 'a' be the first term and common difference be 'd'.
By the formula
S= 2 n (2a+(n-1)d)
S=9(a+4d)
Since the terms are natural number therefore 'd' is also a natural number.
Hence S is divisible by 9.
Therefore S can be 207 or 216.
So (a+4d)=23/24
Now a+d=12
or, a=12-d
Thus (12-d+4d)=23/24
or, (12+3d)=23/24
or, 3(4+d)=23/24
As S should be divisible by 3 thus S =24 or, 4+d=8
d=4
a= 8