Answer:

✏️SEQUENCES

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Question: Which term of the arithmetic sequence is 79, given that the first term is -56 and the second term is -47?

Solution: Determine the common difference of the sequence.

\begin{gathered} \begin{aligned} & \bold{Formula:} \\ & \boxed{d = a_n - a_{n-1}} \end{aligned} \end{gathered}

Formula:

d=a

n

−a

n−1

d = a_2 - a_1 = \text-47 - (\text-56) = 9d=a

2

−a

1

=-47−(-56)=9

» Using the "Arithmetic Sequence Formula", find the term in which 79 is placed.

Given:

a_n = 79 \:;\: n = \:?a

n

=79;n=?

a_1 = \text-56a

1

=-56

d = 9d=9

\begin{gathered} \begin{aligned} & \bold{Formula:} \\ & \boxed{a_n = a_1 + d(n-1)} \end{aligned} \end{gathered}

Formula:

a

n

=a

1

+d(n−1)

79 = \text-56 + 9(n - 1)79=-56+9(n−1)

79 = \text-56 + 9n - 979=-56+9n−9

79 = \text-65 + 9n79=-65+9n

9n = 79 + 659n=79+65

9n = 1449n=144

\begin{gathered} \frac{\cancel9n}{\cancel9} = \frac{144}{9} \\ \end{gathered}

9

9

n

=

9

144

n = 16n=16

\therefore∴ The number 79 is in the:

\Large \underline{\boxed{\tt \purple{ 16^{th} \: term}}}

16

th

term

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