Write a formula for the general term

Question

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for a_n to find a₂₀, the 20th term of the sequence.

 

2, 5, 8, 11,....

 

a_n =      ?      

Answer 1

For the arithmetic sequence 2, 5, 8, 11, ... the common difference, d, is 3 since 5-2 = 3, 8-5 =3, 11-8=3, etc.

 

a₁ = first term = 2

 

a_n = a₁ + (n - 1)d  = 2 + (n - 1)(3)

                                = 3n - 1

 

So, a_{20 =} 3(20) - 1 = 59