Question

(iii)in an ap
given a = 4, d = 2, S = -14, find n and a. ​

Answer 1

Step-by-step explanation:

Given a=2.

d=8

S

n

=90

⇒

2

n

(2a+(n−1)d)=90

⇒

2

n

(2.2+(n−1)8)=90

⇒

2

n

(4+8(n−1))=90

⇒

2

n

(4+8n−8)=90

⇒

2

n

(8n−4)=90

⇒

2

n

(8n−4)=90

⇒4n

2

−2n=90

⇒2n

2

−n=90

⇒2n

2

−n=45

⇒2n

2

−n−45=0

⇒2n

2

−10n−9n−45=0

⇒2n(n−5)9(n−5)=0

⇒(2n+9)(n−5)=0

⇒m=

2

−9

or n=5

Hence n=-9/2 is neglect since n is not negative

∴ n=5

and a

n

=a+(n−1)d

a

5

=a+(5−1)d

=2+4.8

=2+32

=34