Go to the next page to start putting what you have learnt into practice. Thus, it can be written as or it can also be expressed in fractions.Įxpress as a fraction in their lowest terms. is a recurring decimal because the number 2345 is repeated periodically. is a recurring decimal because the number 2 is repeated infinitely. Question Find the sum of each of the geometric seriesįinding the sum of a Geometric Series to InfinityĬonverting a Recurring Decimal to a Fractionĭecimals that occurs in repetition infinitely or are repeated in period are called recurring decimals.įor example, 0.22222222. Find the common ratio and the first term of the geometric series. įinding the number of terms in a Geometric Progressionįind the number of terms in the geometric progression 6, 12, 24. The sum to infinity of the series is 125. A geometric sequence is an ordered set of numbers that progresses by multiplying or dividing each term by a common ratio. Write down the 8th term in the Geometric Progression 1, 3, 9. Write down a specific term in a Geometric Progression To find the nth term of a geometric sequence we use the formula:įinding the sum of terms in a geometric progression is easily obtained by applying the formulas: The geometric sequence has its sequence formation: Note that after the first term, the next term is obtained by multiplying the preceding element by 3. is a geometric sequence with a common ratio of 7 and first term 2. The geometric sequence is sometimes called the geometric progression or GP, for short.įor example, the sequence 1, 3, 9, 27, 81 is a geometric sequence. Geometric Series: the expression for the sum of the terms of a geometric sequence. What are 2 examples of geometric sequence 2, 14, 98, 686. The common ratio (r) is obtained by dividing any term by the preceding term, i.e., Geometric Progression, Series & Sums IntroductionĪ geometric sequence is a sequence such that any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r.
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