Series and common ratios

Question

If the first term of a series is 2 and the 6th term is 10:

a) what is the comoon difference

b) what is the common ratio

 

thank you.

Answer 1

For an arithmetic sequence:

 

a_n = a₁ + (n - 1)d, where a₁ = first term, n = number of terms, d = common difference

 

10 = 2 + (6 - 1)d

8 = 5d

8/5 = d

 

For a geometric sequence.

 

a_n = a₁(r)^n-1, where r = common ratio

 

10 = 2(r)⁵

5 = r⁵

⁵√5 = r