What is the 6th term when An = 2An-1 + n if the first term is 1

Question

please help! Stats btw

Answer 1

For n = 1, A₁ = 1

For n = 2, A₂ = 2A₁ + 2 = 2(1) + 2 = 4

For n = 3, A₃ = 2A₂ + 3 = 2(4) + 3 = 11

For n = 4, A₄ = 2A₃ + 4 = 2(11) + 4 = 26

For n = 5, A₅ = 2A₄ + 5 = 2(26) + 5 = 57

For n = 6, A₆ = 2A₅ + 6 = 2(57) + 6 = 120

Answer 2

This one is a fairly simple plug and chug type of problem.

We know A₁ = 1

This means A₂ = 2A_2-1+2 = 2A₁+2 = 2*1+2 = 4

By extension, we get the following:

A₃ = 2A₂+3 = 2*4 + 3 = 11

A₄ = 2A₃+4 = 2*11+4 = 26

A₅ = 2A₄+5 = 2*26+5 = 57

Finally, we can calculate the sixth term of our sequence (A₆):

A₆ = 2A₅+6 = 2*57+6 = 120