college algebra word problem

Question

Write the first four terms of the sequence defined by the recursive formula a₁ = 4, a_n = a_n−1 + n.

Answer 1

Hello, thank you for taking the time to post your question!

We’re given that

a_1 = 4 , so that is the first term

to find the second term then, I would plug in n = 2

a_2 = a_1 + n = 4 + 2 = 6

then you can keep applying that pattern from there

a_3 = a_2 + n = 6 + 3 = 9

a_4 = a_3 + n = 9 + 4 = 13

meaning that the first four terms of the sequence are 4, 6, 9, and 13.

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

a2 = a1+2 = 4+2=6

a3 = a2+3 = 6+3=9

a4 = a3+4 = 9+4 = 13

a5 = a4+5= 13+5 = 18