Question

Indicate the general rule for this sequence. Find a 1 and the common difference. a 4 = 18 a 7 = 9

Answer 1

The general rule for the sequence is an = -9 + (n-1)(9). The first term (a1) is -9 and the common difference is 9.

Step-by-step explanation:

Sequence Analysis:

To find the general rule for a sequence, we need to determine the pattern or relationship between the terms. In this case, we are given a4 = 18 and a7 = 9. To find the common difference, we subtract the two terms: 18 - 9 = 9. So, the common difference is 9. To find a1, we can use the formula: an = a1 + (n-1)d, where n is the term number and d is the common difference. Substituting n = 4, a4 = 18, and d = 9, we can solve for a1. 18 = a1 + (4-1)(9), which gives us a1 = 18 - 3(9) = 18 - 27 = -9. Therefore, the general rule for this sequence is an = -9 + (n-1)(9). The first term (a1) is -9 and the common difference is 9.

Answer 2

If
`d` is the common difference in an arithmetic sequence, whose
`n`-th term is
`a_n`, then


`a_7=a_6+d`

`a_6=a_5+d`

`a_5=a_4+d`


`\implies a_7=a_4+3d`

We have


`9=18+3d\implies3d=-9\implies d=-3`