Question

Given: a
n
​
=4,d=2, S
n
​
=−14, Find n and a.

Answer 1

Answer:

⇒a

n

=4

⇒S

n

=−14

⇒d=2

⇒a

n

= a+(n−1)d=4,

⇒a+(n−1)2=4,

⇒a+2n=6,a=6−2n.

⇒S

n

=

2

n

[2a+(n−1)d]

⇒−14=

2

n

[2a+(n−1)2]

⇒−14=n[a+(n−1)]

⇒−14=n[6−2n+n−1]

⇒−14=n[5−n]

⇒−14=5n−n

2

⇒n

2

−5n−14=0

⇒n

2

−7n+2n−14=0

⇒(n+2)(n−7)=0

∴n



=−2

⇒n=7

⇒a=6−2(7)=−8

Answer 2

Answer:

⇒a

n

=4

⇒S

n

=−14

⇒d=2

⇒a

n

= a+(n−1)d=4,

⇒a+(n−1)2=4,

⇒a+2n=6,a=6−2n.

⇒S

n

=

2

n

[2a+(n−1)d]

⇒−14=

2

n

[2a+(n−1)2]

⇒−14=n[a+(n−1)]

⇒−14=n[6−2n+n−1]

⇒−14=n[5−n]

⇒−14=5n−n

2

⇒n

2

−5n−14=0

⇒n

2

−7n+2n−14=0

⇒(n+2)(n−7)=0

∴n



=−2

⇒n=7

⇒a=6−2(7)=−8