(viii) given a = 4, d=2, S = -14, find n and a.
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an= 4
d= 2
Sn=-14
a=?
n=?
an = a+(n-1)d
4 = a + ( n-1)2
4 = a + 2n - 2
6 = a + 2n
6 -2 n = a .........(1)
Sn= n/2 ( a + an )
-14 = n/2 ( 6-2n + 4 )
-28 = n ( 10 -2n )
-28= 10n -2n^2
2n ^2 -10n -28 =0
Divide by 2
n^2 -5n -14 =0
n ^2 -7n +2n -14 =0
n ( n-7) + 2 ( n-7)=0
( n-7) ( n+2)=0
n=-2 And n = 7
n is neither be negative. Putting n=7 in equation. (1)
a= 6- 2(7)
a= 6 -14
a= -8
Therefore, a=-8 & n=7
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