Class 10 Maths1)If p, q, r and s are in A.P. then r – q is
s – r
Since p, q, r, s are in A.P.
∴ (q – p) = (r – q) = (s – r) = d (common difference)
Class 10 Maths2)If the sum of three numbers in an A.P. is 9 and their product is 24, then numbers are
2,3,4
Let three numbers be a – d, a, a + d
∴ a – d +a + a + d = 9
⇒ 3a = 9
⇒ a = 3
Also (a – d) . a . (a + d) = 24
⇒ (3 -d) .3(3 + d) = 24
⇒ 9 – d² = 8
⇒ d² = 9 – 8 = 1
∴ d = ± 1
Hence numbers are 2, 3, 4 or 4, 3, 2
Class 10 Maths3)The sum of all two digit odd numbers is
2475