The AP is 9, 17, 25,.......
a (first term) = 9
d (common difference) = 17-9 = 8
Let n be the required number of terms.
Sn (sum of the n terms) = 450
We know that Sn = n/2 (2a + (n-1)d )
450 = n/2 (18 + (n-1)8 )
900 = n(18 + 8n -8)
900 = 8n2 + 10n
8n2 + 10n -900 = 0
8n2 +80n -90n -900 = 0
8n (n +10) -90 (n- 10) = 0
(n-10)(8n-90) = 0
n = 10 or 11.25
But n has to be a natural, since number of terms is always a natural number.
Thus, the required number of terms is 10.