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1 solution
This is an arithmetic-geometric progression in the form:
r × ∑ k = 1 n ( a + ( k − 1 ) d ) r k − 1 = 1 − r a r − [ a + ( n − 1 ) d ] r n + 1 + ( 1 − r ) 2 d r 2 ( 1 − r n − 1 ) .
Setting a = 1 , d = 2 , r = 3 , n = 1 2 produces:
− 2 − 2 3 × 3 1 3 + 3 + 4 1 8 × ( 1 − 3 1 1 ) = 1 7 5 3 7 5 5 6