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In an arithmetic progression, the 30th term is 389, and the 14th term is 181.  Find the sum of the first 25 terms.

 Jun 22, 2020
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Formula for the nth term of an arithmetic progression:  tn  =  t1 + (n - 1)d

--->   389  =  t1 + (30 - 1)d   --->   389  =  t1 + 29d

--->   181  =  t1 + (14 - 1)d   --->   181  =  t1 + 13d

Subtracting:                                  208  =  16d

                                                        13  =  d

 

To find the first term:     181  =  t1 + 13d   --->   181  =  t1 + 13(13)

                                                                          181  =  t1 + 169

                                                                            12  =  t1

 

Now, you know that  t1 = 12  and  d = 13,

use this formula to find the 25th term:   tn  =  t1 + (n - 1)d

 

And use this formula to find the sum of the first 25 terms:  Sum  =  n( t1 + tn ) / 2

where  n  is the number of terms

          t1  is the value of the first term

          tn  is the value of the last term.

 Jun 22, 2020

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