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  • Write the first five terms of each of the sequences in Exercises 11 to 13 and obtain the corresponding series: a1 = 3, an = 3an – 1 + 2 for all n > 1

11.   Write the first five terms of each of the sequences in Exercises 11 to 13 and obtain the corresponding series:   

         a_1 = 3, a_n = 3a_{n - 1} + 2\: \: for \: \: all \: \: n > 1

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Given : a_1 = 3, a_n = 3a_{n - 1} + 2\: \: for \: \: all \: \: n > 1

a_2 = 3a_{2 - 1} + 2=3a_1+2=3(3)+2=11

a_3 = 3a_{3 - 1} + 2=3a_2+2=3(11)+2=35

a_4 = 3a_{4 - 1} + 2=3a_3+2=3(35)+2=107

a_5 = 3a_{5 - 1} + 2=3a_4+2=3(107)+2=323

Hence, five terms of series are 3,11,35,107,323

Series =3+11+35+107+323+...............

Posted by

seema garhwal

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