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# Arithmetic Sequences trouble

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I have no idea how to find a (the first term) or d (the common difference between two successive pairs of terms).

The sum of the first two terms of an arithmetic sequence is 16. The sum of the second and third terms is 28. What are the first three terms of the sequence?

Guest Mar 5, 2017
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Let a1 be the first term

Then the second term is  a1 + d

And the third term is  a1 + 2d

So we have

a1 + [ a1 + d ] = 16    →    2a1 + d  = 16   →   d  =  16 - 2a1      (1)

[a1 + d] + [a1 + 2d]  =  28    →  2a1 + 3d =  28      (2)

Sub  (1)  into (2)   and we have

2a1 + 3 [16 - 2a1]   = 28

-4a1  + 48   =  28       subtract 48 from both sides

-4a1  = -20     divide both sides by -4

a1  = 5

And using (1).....d = 16 - 2(5)   =  16 - 10  = 6

So  the first term  =  5

The second term is 11

And the third term = 17

CPhill  Mar 5, 2017

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