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Find the first four terms of the sequence defined by a1 = 3 and an = 3an–1 + 2, for all n > 1.
Find the first four terms of the sequence defined by a1 = 3 and an = 3an–1 + 2, for all n > 1.
Arithmetic Progressions | CBSE | Class 11 | Exercise 19.1 | Maths | RD Sharma
Find the first four terms of the sequence defined by a1 = 3 and an = 3an–1 + 2, for all n > 1.

Answer:

Using n = 1, 2, 3, 4, the first four terms can be calculated.

If n = 1,

a1 = 3

If n = 2,

a2 = 3a2–1 + 2

a2 = 3a1 + 2

a2 = 3(3) + 2

a2 = 9 + 2

a2 = 11

If n = 3,

a3 = 3a3–1 + 2

a3 = 3a2 + 2

a3 = 3(11) + 2

a3 = 33 + 2

a3 = 35

 

If n = 4,

a4 = 3a4–1 + 2

a4 = 3a3 + 2

a4 = 3(35) + 2

a4 = 105 + 2

a4 = 107

∴ First four terms of sequence = 3, 11, 35, 107.

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