Write the first five terms of the sequence defined by the recursive formula an=2*(an-1)+3 with a1=-2

The required first five terms is 5,7,9,11,13 of the sequence defined by the recursive formula,  with .

Given that,

Recursive formula; with

We have to determine,

The first five terms of sequence defined by recursive formula;

According to the question,

Recursive formula; ,

The first term of the sequence,

The second term of the sequence,

The third term of the sequence,

The fourth term of the sequence,

The fifth term of the sequence,

Hence, The required first five terms is 5,7,9,11,13 of the sequence defined by the recursive formula,  with .

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The first five terms of the sequence are 5, 7, 9, 11 and 13.

Step-by-step explanation:

The first five terms of the sequence are:

a₁ = 2 * (2 - 1) + 3 = 2 * 1 + 3 = 2 + 3 = 5

a₂ = 2 * (3 - 1) + 3 = 2 * 2 + 3 = 4 + 3 = 7

a₃ = 2 * (4 - 1) + 3 = 2 * 3 + 3 = 6 + 3 = 9

a₄ = 2 * (5 - 1) + 3 = 2 * 4 + 3 = 8 + 3 = 11

a₅ = 2 * (6 - 1) + 3 = 2 * 5 + 3 = 10 + 3 = 13

The first five terms of the sequence are 5, 7, 9, 11 and 13.

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step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2