Let be in an A.P. with common difference . If the standard deviation of is and mean is , then is equal to:

34 Explanation: Solution Given the sequence is in Arithmetic Progression (A.P.) with: First term Number of terms Common difference Step 1: Find the Common Difference ( ) The formula for the variance ( ) of an A.P. with terms and common difference is: Given standard deviation , so variance . (We take because implies ). Step 2: Calculate the Mean ( ) For an A.P. with an odd number of terms, the mean is equal to the middle term ( ): Step 3: Find the Sixth Term ( ) Step 4: Calculate Correct Option: (4)

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

Let $9 = x_1 < x_2 < \dots < x_7$ be in an A.P. with common difference $d$ . If the standard deviation of $x_1, x_2, \dots, x_7$ is $4$ and mean is $\bar{x}$ , then $\bar{x} + x_6$ is equal to:

JEE 2023 — Mathematics PYQ

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