Sum of 4 arithmetic means between 3 and 23 is
Sum of 4 arithmetic means between 3 and 23 is
A) 69
B) 48
C) 52
D) 50
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Correct option is (C) 52
Let 4 arithmetic means between 3 and 23 are a+d, a+2d, a+3d and a+4d.
\(\therefore3,a+d,a+2d,a+3d,a+4d,23\) will form an A.P.
\(\therefore\) a = 3 and a+5d = 23
\(\Rightarrow5d=23-a\)
\(=23-3=20\)
\(\Rightarrow d=\frac{20}5=4\)
\(\therefore\) Sum of 4 arithmetic means
= (a+d) + (a+2d) + (a+3d) + (a+4d)
\(=4a+10d\)
\(=4\times3+10\times4\) \((\because a=3\;\&\;d=4)\)
\(=12+40=52\)
Hence, sum of 4 arithmetic means between 3 and 23 is 52.
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