a=3,d=7,Sn=123 find a and an
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Sn =n/2 into 2a+(n-1) d
Therefore, put the values of Sn, a and d.
123=n/2 into (2into3+(n-1) 7)
123=n/2 into (6+7n-7)
123=n/2 into (7n-1)
123 into 2= n(7n-1)
246=7n square-n
7n square -n-246=0 -246into7 factors
7n square- 42n+41n-246=0 are -42 and 41.
7n(n-6)-41(n-6)=0
(7n-41)(n-6)=0
7n=41/n=6
n=41/7/n=6
n=5.85/n=6
But, the sequence is never an integer.
Therefore,n=6
a=3( given )
an=3 into 6
an=18.
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