What is the 29th term of -36 -32-28 -24

Question

Arithmetic sequence

Answer 1

First, we must find a general pattern for this sequence. Looking at the first few, we can see that each term is four more than the previous one.

If we let a_i denote the i-th term in the sequence, then

a_1 = -36

a_2 = a_1 + 4 = a_1 + 4*1 = -32

a_3 = a_2 + 4 = (a_1 + 4) + 4 = a_1 + 4*2 = -28

a_4 = a_3 + 4 = (a_1 + 2(4)) + 4 = a_1 + 4*3 = -24

And so on. From this, we can see the pattern. In general, we see that

a_i = a_1 + 4*(i-1) = -36 + 4*(i-1)

Therefore, the 29th term in the sequence is

a_{29} = -36 + 4*(29-1) = -36 + 4*28 = -36 + 112 = 76.