Question

HELP PLEASE!!! The fourth term in an arithmetic sequence is 19 and the sixth term is 27. If the first term is a1, which is an equation for the nth term of this sequence

Answer 1

The nth term = a1 + 4(n - 1).

Explanation:

The value of the 6th term - the values of the fourth = 2 * common difference (d).

So, d = 27 - 19 = 2d giving d = 8/2 = 4.

The nth term is an = a1 + 4(n - 1).

To find the value of a1 we use the knowledge that a4 = 19

Taking 4 away from this gives us the 3rd term = 15. To get a1 we need to take another 2 4's away. This gives us 15-8 = 7.

So the nth term = 7 + 4(n - 1).

Answer 2

an =7+4(n-1)

Explanation:

an =a1+ d(n-1) is the equation for an arithmetic sequence

When n=4 an =19

19 =a1 + d(4-1)

19 =a1 + d(3)

When n =6 an =27

27 = a1 +d*(6-1)

27 = a1 +d*5

Now we have 2 equations and 2 unknowns

19 =a1 + d(3)

27 = a1 +d*5

Subtract them to eliminate a1

27 = a1 +d*5

-19 =a1 + d(3)

-----------------------

8 = 2d

Divide by 2

8/2 = 2d/2

4 =d

The common difference is 4

Now we need to find a1

27 = a1 +d*5

27 = a1 + (4) *5

27 = a1+ 20

Subtract 20 from each side

27-20 =a1 +20-20

7 =a1

The initial term is 7

an = a1+ d(n-1)

an =7+4(n-1)