In an arithmetic sequence, a17 = -40 and
a28 = -73. Explain how to use this information to write a recursive formula for this sequence.
please answer!

= -40

a + 16d = -40 ...... -(i)

= -73

a + 27d = -73 .......(ii)

Subtracting (i) and (ii)

a + 16 d - a - 27 d = - 40 + 73

-11d = 33

d = -3

a = -40 - 16d = -40 - 16(-3) = 8

= 8 + (n-1)-3

= 8 -3n +3

= -3n + 11

Hence recursive formula :

= -3n + 11

Step-by-step explanation:

We are given the values of two terms in this arithmetic sequence: and . We want to find the recursive formula of this sequence, which will be in the form , where is the first term and d is the common difference.

Here, we can pretend that will replace the term, while replaces the term. This way, n becomes 28 and 1 becomes 17. Now, we can write:

Substitute in the values we know:

Solve for d:

11d = -33

d = -3

Now, we need to find our first term. We can do this by replacing with again, but this time, we're actually going to use :

Plug in the values we know:

Solve for :

-73 = - 81

= 8

Put these altogether:

Thus, the recursive formula is .

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