Ineed , arithmetic sequences always mess me up

Missing term of the sequence is 399.

Step-by-step explanation:

In the given table we will try to find the sequence in terms of y and x parameters.

Since y = 3, 12, 21, 30, it's an arithmetic progression then we can represent nth term of this sequence as y = a + (x-1)d where a = first term, x = number of terms and d = common difference.

y = 3 + (x-1)×d = 3 + (x-1)×9 = 3 + 9x -9 = (9x - 6)

Now we have to find the term x = 45 ( 45th term)

By putting the value of x = 45 in the equation we will find the value of y.

y = 9×45 - 6 = 405 -6 = 399

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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