Question

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

Answer 1

Answer:

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.

Answer 2

The required first five terms is 5,7,9,11,13 of the sequence defined by the recursive formula, $a_n = 2(a_n-1)+ 3$  with $a_1 = -2$.

Given that,

Recursive formula; $a_n = 2(a_n-1)+ 3$ with $a_1= -2$

We have to determine,

The first five terms of sequence defined by recursive formula;

According to the question,

Recursive formula; $a_n = 2(a_n-1)+ 3$,

The first term of the sequence,

$a_n = 2(a_n-1)+ 3\\a_1= 2(2-1)+ 3\\a_1 = 5+ 3\\a_1 = 5$

The second term of the sequence,

$a_2 = 2 \times (3 - 1) + 3\\a_2 = 2 \times 2 + 3 \\a_2= 4 + 3 \\a_n= 7$

The third term of the sequence,

$a_3 = 2 \times (4 - 1) + 3 \\a_2= 2 \times 3 + 3 \\a_2 = 6 + 3 \\a_2= 9$

The fourth term of the sequence,

$a_4 = 2 \times (5 - 1) + 3 \\a_4= 2 \times4 + 3 \\a_4= 8 + 3\\a_4 = 11$

The fifth term of the sequence,

$a_5 = 2 \times (6 - 1) + 3 \\a_5 = 2 \times 5 + 3 \\a_5= 10 + 3 \\a_5= 13$

Hence, The required first five terms is 5,7,9,11,13 of the sequence defined by the recursive formula, $a_n = 2(a_n-1)+ 3$  with $a_1 = -2$.

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