Q. 164.1( 7 Votes )

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Answer :

Given: S5 + S7 = 167


S10 = 235


To find: S20


Formula Used:


Sum of “n” terms of an AP:



Where Sn is the sum of first n terms


n = no of terms


a = first term


d = common difference


Explanation:


Let the first term, common difference and the number of terms of an AP are a, d and n, respectively.


As,


S5 + S7 = 167



we have,



5(2a + 4d) + 7( 2a + 6d ) = 334


10a + 20d + 14a + 42d = 334


24a + 62d = 334


12a + 31d = 167


12a = 167 - 31d [ eqn 1]


Also,


S10 = 235



5[ 2a + 9d] = 235


2a + 9d = 47


12a + 54d = 282 [ multiplication by 6 both side]


167 - 31d + 54d = 282 [ using equation 1]


23d = 282 - 167


23d = 115


d = 5


using this value in equation 1


12a = 167 - 31(5 )


12a = 167 - 155


12a = 12


a = 1


Now




= 10[ 2 + 95]


= 970


So, the sum of first 20 terms is 970.


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