Answer:
-160.
Explanation:
To find the 25th term (a25) of the sequence using the recursive formula, we first need to identify the general recursive rule.
In this sequence, the common difference between consecutive terms is -8. This means that to get from one term to the next, we subtract 8.
The recursive formula for an arithmetic sequence is:
an = an-1 + d
where:
an is the nth term,
an-1 is the previous term (the (n-1)th term),
d is the common difference.
For this specific sequence, a1 = 32 (the first term) and d = -8 (the common difference).
Now, we can use the recursive formula to find a25:
a2 = a1 + d = 32 - 8 = 24
a3 = a2 + d = 24 - 8 = 16
a4 = a3 + d = 16 - 8 = 8
At this point, we can see that the sequence is decreasing by 8 at each step. We can continue this pattern until we find the 25th term.
a5 = a4 + d = 8 - 8 = 0
a6 = a5 + d = 0 - 8 = -8
a7 = a6 + d = -8 - 8 = -16
a8 = a7 + d = -16 - 8 = -24
a9 = a8 + d = -24 - 8 = -32
And so on...
It's clear that the sequence continues decreasing by 8 for each term. Eventually, we will reach a25.
a25 = a24 + d = ???
We can continue this process until we find a25:
a10 = a9 + d = -32 - 8 = -40
a11 = a10 + d = -40 - 8 = -48
a12 = a11 + d = -48 - 8 = -56
a13 = a12 + d = -56 - 8 = -64
a14 = a13 + d = -64 - 8 = -72
a15 = a14 + d = -72 - 8 = -80
a16 = a15 + d = -80 - 8 = -88
a17 = a16 + d = -88 - 8 = -96
a18 = a17 + d = -96 - 8 = -104
a19 = a18 + d = -104 - 8 = -112
a20 = a19 + d = -112 - 8 = -120
a21 = a20 + d = -120 - 8 = -128
a22 = a21 + d = -128 - 8 = -136
a23 = a22 + d = -136 - 8 = -144
a24 = a23 + d = -144 - 8 = -152
Finally, we have found a24. Now, we can find a25:
a25 = a24 + d = -152 - 8 = -160
So, the 25th term (a25) of the sequence is -160.