SOLUTION: If the 4th term of an arithmetic series is 62 and the 14th term is 122. Determine the sum of the first 30 terms.

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Question 1010798: If the 4th term of an arithmetic series is 62 and the 14th term is 122. Determine the sum of the first 30 terms.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
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If the 4th term of an arithmetic series is 62 and the 14th term is 122, determine the sum of the first 30 terms.
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From the condition, we have two equations for 4-th and 14-terms of the AM:

  =  62   and
 = 122.

Or

  =  62,   (1)
 = 122.   (2)

Distract the equation (1) from the equation (2). You will get

10*d = 122 - 62 = 60.

Hence, d = 6. Thus the common difference of the given AM is 6.

Having this, you can easily find the first term of the AM from (1). It is

 = 62 - 3*6 = 44.

Now, when you know everything about the given AM, you can easily calculate the sum of the first n terms. 
Use the formula for the sum of the first n terms of arithmetic progression
(see the lesson Arithmetic progressions in this site). The sum is 

 =  =  = 3930.


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