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A series is 93, 150, 212, 283, 379, 536,...

A series is 93, 150, 212, 283, 379, 536, 818. Another series is 113, __, __, __, __, __. M. Which follows same pattern as given number series. Then m= ?

A

399

B

443

C

536

D

838

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to identify the pattern in the first series and then apply that pattern to the second series starting with 113. **Step 1: Identify the differences in the first series.** The first series is: 93, 150, 212, 283, 379, 536, 818. - The difference between 150 and 93 is: \( 150 - 93 = 57 \) - The difference between 212 and 150 is: \( 212 - 150 = 62 \) - The difference between 283 and 212 is: \( 283 - 212 = 71 \) - The difference between 379 and 283 is: \( 379 - 283 = 96 \) - The difference between 536 and 379 is: \( 536 - 379 = 157 \) - The difference between 818 and 536 is: \( 818 - 536 = 282 \) **Step 2: List the differences.** The differences we found are: 57, 62, 71, 96, 157, 282. **Step 3: Find the second differences.** Now, we will find the differences of these differences: - \( 62 - 57 = 5 \) - \( 71 - 62 = 9 \) - \( 96 - 71 = 25 \) - \( 157 - 96 = 61 \) - \( 282 - 157 = 125 \) The second differences are: 5, 9, 25, 61, 125. **Step 4: Find the third differences.** Next, we will find the differences of these second differences: - \( 9 - 5 = 4 \) - \( 25 - 9 = 16 \) - \( 61 - 25 = 36 \) - \( 125 - 61 = 64 \) The third differences are: 4, 16, 36, 64. **Step 5: Identify the pattern in the third differences.** The third differences are perfect squares: - \( 2^2 = 4 \) - \( 4^2 = 16 \) - \( 6^2 = 36 \) - \( 8^2 = 64 \) This suggests that the next difference should be \( 10^2 = 100 \). **Step 6: Calculate the next difference.** Now, we can add this to the last second difference: - \( 125 + 100 = 225 \) **Step 7: Calculate the next first difference.** Now, we add this to the last first difference: - \( 282 + 225 = 507 \) **Step 8: Calculate the next term in the first series.** Now, we add this to the last term in the first series: - \( 818 + 507 = 1325 \) **Step 9: Find the second series.** Now we apply the same pattern to the second series starting with 113: - The first term is 113. - The first difference is 57: \( 113 + 57 = 170 \) - The second difference is 62: \( 170 + 62 = 232 \) - The third difference is 71: \( 232 + 71 = 303 \) - The fourth difference is 96: \( 303 + 96 = 399 \) - The fifth difference is 157: \( 399 + 157 = 556 \) - The sixth difference is 282: \( 556 + 282 = 838 \) Thus, the value of M is: **M = 838.**
To solve the problem, we need to identify the pattern in the first series and then apply that pattern to the second series starting with 113. **Step 1: Identify the differences in the first series.** The first series is: 93, 150, 212, 283, 379, 536, 818. - The difference between 150 and 93 is: \( 150 - 93 = 57 \) ...
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