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SEQUENCES AND SERIES
QUESTION 1: The 8th and 20th terms of an arithmetic sequence are respectively equal to
the 6th and 8th terms of a geometric sequence. In the arithmetic sequence the first term is
a and the non-zero common difference d, whilst r is the common ratio in the geometric
sequence.
(a) Show that r^2=a+19d/a+7d
(b) If the 5th term of the arithmetic sequence is 4 and r is an integer, determine all
possible General Terms of both sequences.

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Answer:

Step-by-step explanation:

As we Know that formula for arithmetic sequence is

[tex]a_n=a_1+(d-1)[/tex]

and for geometric sequence is

[tex]a_n=a1*r^(n-1)[/tex]

So,

According to given conditions

     [tex]a+7d=a*r^5 (i)\\ a+19d=a*r^7 (ii)[/tex]

By dividing equation (i) and (ii)

Hence proved that

[tex]r^2=a+19d/a+7d[/tex]

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