Question #336146

1.    The first term of an arithmetic series is 1 . the common difference of the series is 6.Find the tenth term of the series if the sum of the first n terms of the series is 7400. Show that 3n^2-2n-7400=0


1
Expert's answer
2022-05-04T11:47:37-0400
a1=1,d=6a_1=1, d=6

an=a1+d(n1)=1+6(n1)a_n=a_1+d(n-1)=1+6(n-1)

Sn=a1+an2n=1+1+6(n1)2nS_n=\dfrac{a_1+a_n}{2}\cdot n=\dfrac{1+1+6(n-1)}{2}\cdot n

=n+3n(n1)=3n22n=n+3n(n-1)=3n^2-2n

Given Sn=7400.S_n=7400.


3n22n=74003n^2-2n=7400

3n22n7400=0,n13n^2-2n-7400=0, n\ge 1

(3n+148)(n50)=0(3n+148)(n-50)=0

Since n0,n\ge 0, we take n=50.n=50.


a50=1+6(501)=295a_{50}=1+6(50-1)=295




a10=1+6(101)=55a_{10}=1+6(10-1)=55


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