SOLUTION: 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.

Algebra.Com
Question 1151205: 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.
Answer by ikleyn(52795)   (Show Source): You can put this solution on YOUR website!
.
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.
~~~~~~~~~~~~~~ 


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,   = 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.    ANSWER

Solved.

RELATED QUESTIONS

In an arithmetic sequence the 8th term is twice the 4th term and the 20th term is 40.... (answered by mananth)
an arithmetic progression has the 8th term being twice the 4th term. if the 20th term is... (answered by mananth)
THE 2ND AND 7TH TERM OF A G.P ARE 18 AND 4374 RESPECTIVELY. FIND THE 1) COMMON... (answered by josgarithmetic,Edwin McCravy,mccravyedwin,ikleyn,AnlytcPhil)
In an arithmetic progression, 8th term is 8 and sum of the first 16 terms is 144. Find... (answered by josgarithmetic)
5th term of an A.P is 9 and the 8th term is 27 find the 6th term and common difference... (answered by ikleyn)
the third term of an A.P is 16 and its 6th term is 34 .find... (answered by ikleyn)
The first term of an A.P is 7 and the sum of the first 40 terms is 1216. Find the nth... (answered by solver91311)
In a geometric progression the sum of 2nd and 4th terms is 30. The difference of 6th... (answered by richwmiller)
In an A.P,the difference between the 8th and 4th term is 20 and the 8th is one and half... (answered by MathTherapy)