The first term of an arithmetic sequence is -30 and the common difference is 8. Find the 20:n term.

n = 15

Explanation:

This is an

Arithmetic sequence

The sum of the first n terms of this sequence is given by.

S

n

=

n

2

[

2

a

+

(

n

−

1

)

d

]

where a is the first term and d , the common difference.

here a = -16 , d = 8 and require to solve for n.

hence :

n

2

[

(

2

×

−

16

)

+

8

(

n

−

1

)

]

=

600

n

2

[

−

32

+

8

n

−

8

]

=

600

⇒

n

2

(

8

n

−

40

)

=

600

distributing gives :

4

n

2

−

20

n

−

600

=

0

Equated to zero since this is a quadratic equation.

⇒

4

(

n

2

−

5

n

−

150

)

=

0

⇒

4

(

n

+

10

)

(

n

−

15

)

=

0

⇒

n

=

−

10

or

n

=

15

but n > 0 hence n = 15

Step-by-step explanation:

[2, 2.5)

(2.5, 3]

step-by-step explanation:

i think its these two not sure [2, 2.5)

(2.5, 3]