Q. 204.4( 7 Votes )

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Answer :

Given: a11 : a18 = 2:3


To find: a5:a21


S5:S21


Formula Used:


Sum of “n” terms of an AP:



Where Sn is the sum of first n terms


nth term of an AP is:


an = a + (n - 1) d


Where an is the last term.


n = no of terms


a = first term


d = common difference


Explanation:


Let “a” and “d” the first term and common difference of an AP.


a11:a18 = 2:3


a + 10d : a + 17d = 2:3



3a + 30d = 2a + 34d


a = 4d [ eqn 1]


a5 = a + 4d = 4d + 4d = 8d [ by eqn 1] [ Eqn 2]


a21 = a + 20d = 4d + 20d = 24d [ by eqn 1] [ Eqn 3]



now using the formula





= 30d





= 21( 14 )d


= 294


S5:S21 = 30 : 294 = 5: 49


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