Algebra 1 Explicit Formulas

Question

a.

2, -10, 50, -25, 1250

b.

12.6, 5.6, -1.4, -8.4, -15.4

What is the explicit formula for each sequence?

a.

2, -10, 50, -25, 1250

a= first term= 2

d=common difference=-10-2 = -12

Therefore,

a_n=a+(n-1)d

a_n=2+(n-1)*(-12)

a_n=2-12n+12

a_n=14-12n

b.

12.6, 5.6, -1.4, -8.4, -15.4

a= first term= 12.6

d= common difference= 5.6-12.6 = -7

Therefore,

a_n=a+(n-1)d

a_n=12.6+(n-1)*(-7)

a_n=12.6-7n+7

a_n=19.6-7n

Is this correct? If not, what do I need to change?

Answer 1

You got problem b) correct but problem a) is not an arithmetic sequence. Although the difference between the first two terms is -12, (2, -10) the difference between the 2nd and 3rd term is 60 (-10, 50). This is a geometric sequence where r = -5

a_n = a₁(r)^n-1 = 2(-5)^n-1

You can also write this as a_n = a₀(r)ⁿ where a₀ is the "zeroth" term, in other word go backwards one step from the first term (so from 2, we divide by -5 to get a₀ = -2/5) so it could be written as a_n = -2/5(-5)ⁿ but you are probably used to the other version a_n = 2(-5)^n-1