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Question 1141683: The twenty first term of an app is five and a half while the sum of the twenty one terms is ninetyfour and a half.find the sum of the first 3 terms of the ap
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! formula for nth term of an arithmetic progression is An = A1 + (n-1) * d
formula for sum of n terms of an arithmetic progression is Sn = n * (A1 + An) / 2
you are given that the 21st term of an arithmetic progression is equal to 5.5.
you are also given that the sum of the first 21 terms of the arithmetic progression is 94.5.
since Sn = n * (A1 + An) / 2, then you get 94.5 = 21 * (A1 + 5.5) / 2.
simplify the equation to get 94.5 = (21 * A1 + 115.5) / 2
multiply both sides of that equation by 2 to get 189 = 21 * A1 + 115.5
subtract 115.5 from both sides of that equation to get 73.5 = 21 * A1
divide both sides of that equation by 21 to get 3.5 = A1.
since An = A1 + (n-1) * d, then A21 = A1 + 20 * d.
since A21 = 5.5 and A1 = 3.5, then 5.5 = 3.5 + 20 * d
subtract 3.5 from both sides of that equation to get 2 = 20 * d.
divide both sides of that equation by 20 to get 2 / 20 = d.
solve for d to get d = .1
you have A1 = 3.5 and d = .1
you want the sum of the first 3 terms of the arithmetic progression.
A1 = 3.5
A2 = 3.5 + 1 * .1 = 3.6
A3 = 3.5 + 2 * .1 = 3.7
since it's only 3 terms, you can just add them up.
sum of the first 3 terms is 3.5 + 3.6 + 3.7 = 10.8.
you can also use the sum of an arithmetic progression formula to get S3 = 3 * (A1 + A3) / 2 = 3 * (3.5 + 3.7) / 2 = 3 * 7.2 / 2 = 3 * 3.6 = 10.8.
your solution is that the sum of the first 3 terms of the arithmetic progression is 10.8.
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