Mathematics, 31.01.2020 18:59 leilanimontes714

Find the third, fourth, and fifth terms of the sequence defined by
a= 4, a2 = 9, and an = 2an − 1 − an − 2 for n ≥ 3.

a3=
a4=
a5=
a6=

Answers: 1

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Answer from: reycaden

By the recursive definition,

$a_3=2a_2-a_1=2\cdot9-4=14$

$a_4=2a_3-a_2=2\cdot14-9=19$

$a_5=2a_4-a_3=2\cdot19-14=24$

$a_6=2a_5-a_4=2\cdot24-19=29$

Answer from: jasminelynn135owmyj1

a3=14, a4=19, a5=24

Step-by-step explanation:

Put the numbers where the symbols are and do the arithmetic.

a3 = 2(a2) -(a1) = 2(9) -4 = 14

a4 = 2(a3) -(a2) = 2(14) -9 = 19

a5 = 2(a4) -(a3) = 2(19) -14 = 24

a6 = 2(a5) -(a4) = 2(24) -19 = 29

With a little work, you can show that this is an arithmetic sequence with a common difference of a2-a1 = 5.

Let d = a[2] -a[1]

Of course, the second term is that difference added to the first:

a[2] = a[1] + (a[2] -a[1]) = a[1] +d

The third term is ...

a[3] = 2a[2] -a[1] = a[2] +(a[2] -a[1]) = a[2] +d

a[4] = 2a[3] -a[2] = a[3] +(a[3] -a[2]) = a[3] -(a[2] +d) -a[2] = a[3] +d

Answer from: Quest

Move the decimal behind it

Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

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Find the third, fourth, and fifth terms of the sequence defined by
a= 4, a2 = 9, and an = 2an...

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