Question

What is the common difference of an arithmetic sequence whose first term is 25 and whose tenth term is 115.

Answer 1

common difference d = 10

Explanation:

the nth term of an arithmetic sequence is

`a_(n)` = a₁ + (n - 1)d

a₁ is the first term, d the common difference , n the term number

given

a₁₀ = 115 , then

a₁ + 9d = 115 ( substitute a₁ = 25 into the equation )

25 + 9d = 115 ( subtract 25 from both sides )

9d = 90 ( divide both sides by 9 )

d = 10

then the common difference is d = 10