![]() 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. įinding the number of terms in a Geometric Progressionįind the number of terms in the geometric progression 6, 12, 24. 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: To find the sum of an infinite geometric series having ratios with an absolute value less than one, use the formula, Sa11r, where a1 is the first term and r. ![]() 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. 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. 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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