Question 998359
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The second and seventh term of a geom. progression are 18 and 4374 respectively find the  (a) common ratio  (b) sum of  4th and 8th terms  (c) sum of the first 10 terms.
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{{{a[2]}}} = {{{a[1]}}}.{{{q}}}   =   18     (1)

{{{a[7]}}} = {{{a[1]}}}.{{{q^6}}} = 4374     (2)


Divide (2) by (1). You will get


{{{q^5}}} = {{{4374/18}}} = 243.


Hence, {{{q}}} = {{{root(5, 243)}}} = 3.


It implies {{{a[1]}}} = {{{a[2]/q}}} = {{{18/3}}} = 6.


Now, when you know {{{a[1]}}} = 6 and {{{q}}} = 3, you can calculate all remaining values.
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