Sequence

The arithmetic sequence is given:

Sn=1656, d=6, an=138

Calculate a1 and n.

Final Answer:

a =  0
n =  24

Step-by-step explanation:

s=1656 d=6 b=138  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⋅ 1656=n⋅ (2⋅ 138−6⋅ (n−1))  2⋅ 1656=n⋅ (2⋅ 138−6⋅ (n−1)) 6n2−282n+3312=0 6=2⋅3 282=2⋅3⋅47 3312=24⋅32⋅23 GCD(6,282,3312)=2⋅3=6  n2−47n+552=0  a=1;b=−47;c=552 D=b2−4ac=472−4⋅1⋅552=1 D>0  n1,2​=2a−b±D​​=247±1​​ n1,2​=247±1​ n1,2​=23.5±0.5 n1​=24 n2​=23  n>0 n=n1​=24 a=b−d⋅ (n−1)=138−6⋅ (24−1)=0

Our quadratic equation calculator calculates it.

n=n1​=24

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