![]() ![]() Ordinary Annuity saving plans and geometric progressions Entertainment problems on geometric progressions Fresh, sweet and crispy problem on arithmetic and geometric progressions One characteristic property of geometric progressions Word problems on geometric progressions Solved problems on geometric progressions My other lessons on geometric progressions in this site are , with the first term and the common ratio is equal toįor some basic and typical problems on geometric progressions see the lesson Problems on geometric progressions under the current topic in this site.įor more word problems on geometric progressions see the lesson Word problems on geometric progressions under the current topic in this site. The sum of the first n terms of the geometric progression, ,. The n-th term of the geometric progression with the first term and the common ratio is It is clear that the formula (3) is true also. Take out of brackets as the common multiplier and then divide both sides by providing is not equal to 1. Now, distract the equality (5) from (4) and cancel the like terms. Multiply both sides of the last equality by the progression common ratio. , is the geometric progression with the first term and the common ratio then the formula for the sum of its first n terms is ![]() Formula for sum of a geometric progressionIf,. , is the geometric progression, you have from the definition (see the lesson Geometric progressions under the current topic in this site)īy applying the last formula again and again you have the chain of equalities ![]() , is the geometric progression with the first term and the common ratio then the formula for the n-th term is Formula for n-th term of a geometric progressionIf,. One is the formula for n-th term of a geometric progression, and another is the formula for sum of the first n terms of a geometric progression. This lesson contains the proofs of the two statements related to geometric progressions (see the lesson Geometric progressions under the current topic in this site). The proofs of the formulas for geometric progressions ![]()
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