Arithmetic Sequence

Question

The first three terms of an arithmetic sequence are 5p,20,3p, where p is constant. Find the 20th term in the sequence!

Answer 1

To be an arithmetic sequence, there must be a common difference, so

20 - 5p = 3p - 20

40 = 8p

p = 5

The common difference is 20-5p=20-5(5)= -5, so the first 3 terms are

25, 20, 15, ...

a₁ = 25

a₂ = a₁ + (2 - 1)(-5) = 20

a₃ = a₁ + (3 - 1)(-5) = 15

Do you see the pattern?

a_n = a₁ + (n - 1)(-5)

Now plug in n=20.