Find five arithmetic means between 1and 19
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Given,
first term (a) = 1
last term (l) = 19
let the five arithmetic mean between 1 and 19 be A₁, A₂, A₃, A₄, A₅
Now,
1, A₁, A₂, A₃, A₄, A₅, 19 are in AP
Number of terms(n)= 5+2 = 7
We know tha last term of AP is given by,
l = a + (n-1)d ( where d is common differecne between the terms)
19 = 1 + (7-1)d
19 = 1 + 6d
18= 6d
d= 3
Again,
A₁ = a + (2-1)d ( as A₁ is second term of AP)
A₁ = 1 + 3
A₁ = 4
Similarly
A₂ = a + 2d
A₂ = 1 + 6
A₂ = 7
A₃ = a + 3d
A₃ = 1 + 3*3
A₃ = 10
A₄ = a + 4d
A₄ = 1 + 4*3
A₄ = 13
A₅ = a + 5d
A₅ = 1 + 5*3
A₅ = 16
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