Mathematics, 18.01.2020 09:31 kerra61

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

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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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Answer from: toopretty15

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 from: Quest

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

Answer from: Quest

the answer is a.

step-by-step explanation:

in three games of golf, alex shot two under par four times.

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

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