Question

Write an explicit formula for each sequence Arithmetic sequences : an=a1+d(n-1) 1) 2, 4, 6, 8 2) 15 , 12, 9 , 6 Geometric sequences : gn=g1 *r (n-1 ) 3) 5, 10 , 20, 40 4) 1, -2 , 4 , -8

Answer 1

1) an=2+2(n-1) OR an=2n

2) an=15-3(n-1) OR an=18-n

3) gn=5(2)^(n-1)

4) gn=1(-2)^(n-1)

Explanation:

1) 2, 4, 6, 8
an will stay as an

a1 is the first term so it will be 2
an=2+d(n-1)

d is the distance between each number which is the same, which is 2.
an=2+2(n-1)

this could also be rewritten as an=2n

2) 15, 12, 9, 6
an will stay as an

a1 is the first term so it will be 15
an=15+d(n-1)

d is the distance between each number which is the same, which will be -3. This is because with each progressing term, the number continues to decrease by 3.
an=15-3(n-1)

this could be rewritten as an=18-n

3) 5, 10, 20, 40
gn stays as gn

g1 is the first term so it will be 5
gn=5(r)^(n-1)

r is the factors that get to the next number. from 5 to 10 is x2; from 10 to 20 is x2, from 20 to 40 is x2. So r would be 2.
gn=5(2)^(n-1)

4) 1, -2, 4, -8
gn stays as gn

g1 is the first term so it will be 1
gn=1(r)^(n-1)

r is the factors that get to the next number. from 1 to -2 is x-2; from -2 to 4 is x-2, from 4 to -8 is x-2. So r would be -2.
gn=1(-2)^(n-1)

Hope this Helped!