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

an =7+4(n-1)

Step-by-step 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)

-9

step-by-step explanation:

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