The terms of this sequence increase by the same amount each time _,_,17_,_,29

9, 13, 17, 21, 25, 29

Step-by-step explanation:

Since there is an equal increase of the same amount, the sequence is arithmetic with n th term

Substituting a = 9 and d = 4 into the n th term expression

= 9 + 4(n - 1) = 9 + 4n - 4 = 4n + 5

= a + (n - 1)d

where a is the first term and d the common difference

The third term and sixth term are therefore

a + 2d = 17 → (1)

a + 5d = 29 → (2)

Subtract (1) from (2) term by term, eliminating a, that is

3d = 12 ( divide both sides by 3 )

d = 4

Substitute d = 4 into either of the 2 equations and solve for a

Substituting into (1)

a + 2(4) = 17

a + 8 = 17 ( subtract 8 from both sides )

a = 9

Thus the first term is 9 and the common difference d = 4

The sequence of terms is therefore

9, 13, 17, 21, 25, 29

Substituting a = 9 and d = 4 into the n th term expression

= 9 + 4(n - 1) = 9 + 4n - 4 = 4n + 5

the answer is b.

step-by-step explanation:

by the trigonometric ratio tangent, tangent equals opposite divided by adjacent.

therefore, tan(50) equals ac/3

multiply each side by 3 to get: ac=3tan(50)

the answer is b.