the first term of an arithematic sequence is 1 and the sum of the first term is 100 find the first term
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Note : This isn't a Biology Question, This question comes under Mathematics,
Here is the solution :
Given that,
First term of A.S = 1,
In general we consider a as the first term,
So, Let a = 1,
Let the next other 3 terms be , b,c,d
According to the Question,
a + b + c + d = 100,
We know the Formula for Sum of n terms of Arthimetic Sequence,
Sn(Sum of n terms) = (n/2)(a+l)
Where a = first term, l = last term, n = no.of terms,
=> 100 = (4/2)(1 + l)
=> 50 = 1 + l,
=> l = 49,
Now, We have to find Common difference(d),
Nth term of A.P = a + (n-1)*d,
=> 49 = 1 + 3*d,
=> 48 = 3d,
=> 16 = d,
=> b = 1 + 16 = 17,
=> c = 17 + 16 = 33,
=> d = 33 + 16 = 49 ✔(This is what we got before)
Therefore : First 4 terms of the A.P are 1 , 17 , 33 , 49