What is the difference between the sum of terms of the A.P and G.P whose first terms are -2+4+....

432

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Did you know that when calculating the sum of terms in an arithmetic progression (A.P) or a geometric progression (G.P) with first terms that are -2+4+..., there is a significant difference? In an A.P, where the numbers increase or decrease by the same fixed amount, the sum of terms can be obtained by multiplying the average of the first and last term by the number of terms. On the contrary, in a G.P, where the terms are obtained by multiplying the previous term by a constant, the sum can be found by multiplying the first term by the ratio of (1 - the common ratio to the power of the number of terms) divided by (1 - the common ratio). These distinct approaches highlight the fundamental dissimilarity between the sum of terms in an A.P and a G.P.