Question

In an A.P, if an = 4, d = 2 and Sn = - 14, then a =
A) 7
B) - 8
C)-2
D)3

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Answer 1

Answer:

Given,

an= 4 , d= 2 , Sn= -14

an= a+(n-1)d

=>4= a + (n - 1) 2

=> 4= a+ 2n -2

=> a=4-2n +2

=> [a=6-2n] ---------------(i)

=>Sn = n/2[2a + (n-1)d]

=>-14= n/2[2×(6-2n)+(n-1)d]

=>-14=n/2[12-4n+2n-2]

=>-14=n/2(10-2n)

=>-14×2= n(10-2n)

=>-28=10n-2n^2

=>2n^2-10n+28=0

=>2(n^2-5n+14)=0

=>n^2-5n+14=0

=>n^2-(7-2)n+14=0

=>n^2-7n+2n+14=0

=>n(n-7) + 2(n-7)=0

=>(n-7)(n+2)=0

.

. . n=7 OR n=-2

Now putting the value of n in (i)

=>a=6-2n

=>a=6-2(7)

=>a=-8

OR

=>a=6-2(-2)

=>a=6+4

=>a=10