Q. 114.3( 77 Votes )

# Write the first five terms of each of the sequences in and obtain the corresponding series:

a_{1} = 3, a_{n} = 3a_{n – 1} + 2 for all n > 1

Answer :

Given here are a_{1} = 3,

a_{n} = 3a(_{n – 1)} + 2…………1

To find out first five terms of the sequence we will put value of n = 2, 3, 4, 5 in 1

a_{2}= 3(3)_{2-1} + 2 = 3 × 3 + 2 = 11

a_{3} = 3a_{2} + 2 = 3 × 11 + 2 = 35 (∵ a_{n-1} = a_{3-1} = a_{2} )

a_{4} = 3a_{3} + 2 = 105 + 2 = 107

a_{5} = 3a_{4} + 2 = 3 × 107 + 2 = 323

Hence the first five terms of the sequence are 3, 11, 35, 107, 323

And the corresponding sequence is 3 + 11 + 35 + 107 + 323 + …….

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