Question 1151205
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in an A.P the 8th term is twice the 4th term and the 20th term is 40.
find the common difference and the sum of terms from the 8th to the 20th.
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<pre>

From the first part of the condition,


    a + 7d = 2*(a + 3d),


where "a" is the 1-st term of the AP and "d" is the common difference.


From this equation


    a + 7d = 2a + 6d,

    7d - 6d = 2a - a

     d      = a.      (1)


We are given also


     a + 19d = 40,


which implies, due to (1)


     20d = 40,

       d = a = 2.


Thus, in this AP the first term is 2 and the common difference is 2, too.


So, the 8-th term is  2+2*7 = 16  and  the 20-th term is  40  (given (!) ).


The average of the 8-th term and the 20-th term is, therefore,  {{{(16+40)/2}}} = 28.


The sum of the terms from the 8-th term to 20-th term (inclusive) is the product of this mean value 28 
by the number of terms, which is (20-7) = 13.


Thus the sum is 28*13 = 364.    <U>ANSWER</U>
</pre>

Solved.