How many terms are there in the AP: 20, 17.5 ..., -25
The common difference in the given arithmetic progression (AP) is -2.5.
To find the number of terms in an AP, we can use the formula:
nth term = a + (n-1)d
where, nth term represents the last term, a represents the first term, n represents the number of terms, and d represents the common difference.
Here, the first term, a = 20 and the common difference, d = -2.5. Let's plug in these values in the formula and solve for n:
-25 = 20 + (n-1)(-2.5)
-25 - 20 = -2.5n + 2.5
-45 = -2.5n
Dividing both sides by -2.5:
(-45) / (-2.5) = n
18 = n
Therefore, there are 18 terms in the given AP: 20, 17.5, ..., -25.