Question

11. if in an A.P n th term is 9-5
n then 10 th term equal to​

Answer 1

Given: a

n

=9−5n

Taking n=1,

a

1

=9−5(1)=9−5=4

Taking n=2,

a

2

=9−5(2)=9−10=−1

Taking n=3,

a

3

=9−5(3)=9−15=−6

Therefore the series is 4,−1,−6,...

So,a=4,d=a

2

−a

1

=−1−4=−5

Now, we have to find the sum of the first 15

th

terms of the AP

S

n

=

2

n

[2a+(n−1)d]

⇒S

n

=

2

15

[2×4+(15−1)(−5)]

⇒S

15

=

2

15

[8−70]

⇒S

15

=

2

15

[−62]

⇒S

15

=15×(−31)

⇒S

15

=−465

Hence, the sum of 15

th

terms is −465.