Question

Given a term in an arithmetic sequence and the common difference, find the first five terms for one of the sequences:

1)a37 = 193, d = 6
2)a32 = 189, d = 5
3)a35 = -312, d = -10
4)a17 = 71, d = 6

Answer 1

For the arithmetic sequence with a37 = 193 and d = 6, the first five terms are -23, -17, -11, -5, 1.

Step-by-step explanation:

For the first sequence: a37 = 193, d = 6

To find the first five terms, we can use the formula:

an = a1 + (n - 1)d

Given that a37 = 193 and d = 6, we can substitute these values into the formula:

a1 + (37 - 1)6 = 193

a1 = 193 - (36)6 = 193 - 216 = -23

So the first term, a1, is -23.

Using the same formula, we can find the next four terms:

a2 = -23 + (2 - 1)6 = -23 + 6 = -17

a3 = -23 + (3 - 1)6 = -23 + 12 = -11

a4 = -23 + (4 - 1)6 = -23 + 18 = -5

a5 = -23 + (5 - 1)6 = -23 + 24 = 1

So the first five terms of the sequence are: -23, -17, -11, -5, 1.