A series is 18, 38, 68, 110, 166, 238. If another series 45, (a), (p), (z), (r), 265 follows the same pattern as the above given series, then which of the following statements is/are correct?
A. Value of p = 95
B. Value of r = 192
C. [(45 +
a) × 0.5] + 40 = p
D. Both A and C E. All A, B and C

ATQ, We observe the differences in the given series: 18 + (4 × 5) = 38 38 + (5 × 6) = 68 68 + (6 × 7) = 110 110 + (7 × 8) = 166 166 + (8 × 9) = 238 So, the pattern is: difference = product of consecutive integers. Now for the new series: 45 45 + (4 × 5) = 65 = a 65 + (5 × 6) = 95 = p 95 + (6 × 7) = 137 = z 137 + (7 × 8) = 193 = r 193 + (8 × 9) = 265 So, a = 65 p = 95 r = 193 Now check the statements: A. p = 95 → Correct B. r = 192 → Incorrect C. [(45 + a) × 0.5] + 40 = p = [(45 + 65) × 0.5] + 40 = [110 × 0.5] + 40 = 55 + 40 = 95 → Correct Therefore, A and C are correct. Hence, Option D is correct.