Arithmetic sequences

Question

Identify the 35th term of an arithmetic sequence where a1=-7 and a18=95

Answer 1

Katelin,

 

There is a nice formula for this problem: a_n = a₁ = (n-1)d, where n = 35 and d is the common difference.

 

You need to start by finding d by using the given information.

 

a₁₈ = a₁ + (18-1)d

95 = -7 + 17d

102 = 17d

d = 102/17 = 6.

 

Going back to the formula and using n = 35, you get

 

a₃₅ = a₁ + (35-1)6 = -7 + 34·6 = 197.

 

Let me know if you have any questions about this.