Q. 204.4( 7 Votes )

The ratio of the 11th term of the 18th term of an AP is 2:3. Find the ratio of the 5th term to the 21st term and also the ratio of the sum of the first five terms to the sum of the first 21 terms.

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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