Sequence

In the arithmetic sequence is given:

Sn=2304, d=2, an=95

Calculate a1 and n.

Correct result:

a =  1
n =  48

Solution:

s=2304 d=2 b=95  b=a+d⋅ (n−1) s=n⋅ (a+b)/2  a=b−d⋅ (n−1) 2s=n⋅ (a+b)  2s=n⋅ (b−d⋅ (n−1)+b)  2∗2304=n∗(2∗95−2∗(n−1))  2⋅ 2304=n⋅ (2⋅ 95−2⋅ (n−1)) 2n2−192n+4608=0  a=2;b=−192;c=4608 D=b2−4ac=1922−4⋅2⋅4608=0 D=0  n1,2=−b±D2a=192±04=48±0 n1,2=48±0 n1=n2=48    Factored form of the equation:  2(n−48)(n−48)=0  n>0 n=n1=48 a=b−d⋅ (n−1)=95−2⋅ (48−1)=1

Our quadratic equation calculator calculates it.

n=n1=48

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