The four arithmetic means between 3 and 23 ar | vedclass

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(B) Let the four arithmetic means be $A_1, A_2, A_3,$ and $A_4$.Then the sequence $3, A_1, A_2, A_3, A_4, 23$ forms an Arithmetic Progression $(AP)$ w

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$7, 11, 15, 19$

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(B) Let the four arithmetic means be $A_1, A_2, A_3,$ and $A_4$.Then the sequence $3, A_1, A_2, A_3, A_4, 23$ forms an Arithmetic Progression $(AP)$ with $n = 6$ terms.The $n^{th}$ term of an $AP$ is given by $T_n = a + (n-1)d$.Here,$a = 3$ and $T_6 = 23$.$23 = 3 + (6-1)d$$23 = 3 + 5d$$20 = 5d$$d = 4$Now,we calculate the means:$A_1 = a + d = 3 + 4 = 7$$A_2 = a + 2d = 3 + 8 = 11$$A_3 = a + 3d = 3 + 12 = 15$$A_4 = a + 4d = 3 + 16 = 19$Thus,the four arithmetic means are $7, 11, 15, 19$.

The four arithmetic means between $3$ and $23$ are

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