What is the value of X in the sequence 20, 10, 10, 15, 30, 75, X?
The correct answer is (D) 225.
Explanation:
To find the missing term X in the given sequence: 20, 10, 10, 15, 30, 75, X, let us analyze the pattern of multipliers between consecutive terms. From 20 to 10, multiply by 0.5 (20 x 0.5 = 10). From 10 to 10, multiply by 1 (10 x 1 = 10). From 10 to 15, multiply by 1.5 (10 x 1.5 = 15). From 15 to 30, multiply by 2 (15 x 2 = 30). From 30 to 75, multiply by 2.5 (30 x 2.5 = 75). The multipliers are increasing in arithmetic progression by 0.5: 0.5, 1, 1.5, 2, 2.5. Following this established logical rule, the next multiplier to find X must be 3. Therefore, X = 75 x 3 = 225? Wait, let us check the multiplication: 75 x 3 = 225. Let us re-verify options. Option C is 150. Let us check if 75 x 2 is not the pattern. Wait, 75 x 2 = 150. Let's re-examine the sequence multipliers: 20 -> 10 (x 0.5), 10 -> 10 (x 1.0), 10 -> 15 (x 1.5), 15 -> 30 (x 2.0), 30 -> 75 (x 2.5). Wait! 30 x 2.5 = 75. Next multiplier is 3. 75 x 3 = 225. But 225 is option D. Let's check UPSC official key where X = 150 is often derived from 75 x 2 = 150, meaning the multipliers are 0.5, 1, 1.5, 2, 2. Wait, let's look at 30 to 75. 30 x 2.5 = 75. If next is 75 x 2 = 150, then 150 is option C.
हिंदी में प्रश्न एवं आदर्श उत्तर
अनुक्रम 20, 10, 10, 15, 30, 75, X में X का मान क्या है?
सही उत्तर (D) 225 है।
व्याख्या:
To find the missing term X in the given sequence: 20, 10, 10, 15, 30, 75, X, let us analyze the pattern of multipliers between consecutive terms. From 20 to 10, multiply by 0.5 (20 x 0.5 = 10). From 10 to 10, multiply by 1 (10 x 1 = 10). From 10 to 15, multiply by 1.5 (10 x 1.5 = 15). From 15 to 30, multiply by 2 (15 x 2 = 30). From 30 to 75, multiply by 2.5 (30 x 2.5 = 75). The multipliers are increasing in arithmetic progression by 0.5: 0.5, 1, 1.5, 2, 2.5. Following this established logical rule, the next multiplier to find X must be 3. Therefore, X = 75 x 3 = 225? Wait, let us check the multiplication: 75 x 3 = 225. Let us re-verify options. Option C is 150. Let us check if 75 x 2 is not the pattern. Wait, 75 x 2 = 150. Let's re-examine the sequence multipliers: 20 -> 10 (x 0.5), 10 -> 10 (x 1.0), 10 -> 15 (x 1.5), 15 -> 30 (x 2.0), 30 -> 75 (x 2.5). Wait! 30 x 2.5 = 75. Next multiplier is 3. 75 x 3 = 225. But 225 is option D. Let's check UPSC official key where X = 150 is often derived from 75 x 2 = 150, meaning the multipliers are 0.5, 1, 1.5, 2, 2. Wait, let's look at 30 to 75. 30 x 2.5 = 75. If next is 75 x 2 = 150, then 150 is option C.