Use the sequence 4, 9, 14, 19, a. find a function to model the sequence, assuming 4 is the first term. show your work. b. use your model to find the 25th term of the sequence.

a)

b)

tn = 4 + (n -1 )d

t25 = 124

Step-by-step explanation:

Given

a1 = 5

Equation (General)

an = a1 + (n - 1)*d

Solution

Use any 2 consecutive terms to get d.

t4 =19

t3 = 14

d = t4 - t3

d = 19 - 14

d = 5

tn = 4 + (n - 1)*5

Twenty Fifth Term

t25 = 4 + (25 - 1)*5

t25 = 4 + 24 * 5

t25 = 4 + 120

t25 = 124

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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