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Q.

Let  Sn denote the sum of the first  n  term of an arithmetic progression. If  S10=390 and the ratio of the tenth and the fifth terms is 15 : 7, then  15(S15−S5) is equal to :

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a

690

b

890

c

158

d

800

answer is C.

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Detailed Solution

102(2a+9d)=390 ⇒2a+9d=78 a+9da+4d=157⇒3d=8a ⇒2a+24a=78 ⇒26a=78 ⇒a=3⇒d=8 ⇒S15=152(6+14(8)) ⇒S15=52(6+4(8)) ⇒S15−S5=15(3+56)−5(3+16) =5(9+168−3−16) =5(158) =790

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