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Insert five arithmetic means between 20 and 32 .

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Let `A_(1), A_(2), A_(3), A_(4) and A_(5)` be the five A.M.'s between 20 32
` therefore 20, A_(1), A_(2), A_(3), A_(4) ,A_(5), 32` are in A.P.
Here a = 20 , n = number of terms of A.P. = 7 , b = 32
Thus` 32 = 20 + (7 - 1 ) d rArr d = 2 `
`therefore A_(1) = a+ d = 20 + 2 = 22 `
` A_(2) = a + 2d = 20 + (2 xx 2) = 24 `
` A_(3) = a + 3d = 20 + ( 3 xx2) = 26 `
`A_(4) = a + 4d = 20 + (4 xx 2 ) = 28 `
` A_(5) = a + 5d = 20 + (5 xx 2 ) = 30 `
Hence, the five A.M.'s between 20 and 32 are 22, 24, 26, 28 and 30 .
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