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Question
Find: `sum_("r" = 1)^10 5 xx 3^"r"`
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Solution
`sum_("r" = 1)^10 5 xx 3^"r"`
= 5 x 3 + 5 x 32 + 5 x 33 + … + 5 x 310
= 5[3 + 32 + 33 + ... + 310]
Here, 3, 32, 33, ..., 310 are the terms in G.P. with
a = 3, r = 3
`sum_("r" = 1)^10 5 xx 3^"r" = 5*(3[3^10 - 1])/(3 - 1)`
= `15/2(3^10 - 1)`
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