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Date:
Day 1
4. F-IF.1.3
Find the first five terms of the recursive sequence defined by the function below.
f(n)=2f(n-1)+3n, where
f(1)=-2
5. F-LE.1.2
The third term in an arithmetic sequence is 10 and the fifth term is 26 . If the first term is
a_(1), which is an equation for the
nth term of this sequence?

Date: $\newline$ Day $1$ $\newline$ $4$ . F-IF. $1$ . $3$ $\newline$ Find the first five terms of the recursive sequence defined by the function below. $f(n)=2 f(n-1)+3 n$ , where $f(1)=-2$ $\newline$ $5$ . F-LE. $1$ . $2$ $\newline$ The third term in an arithmetic sequence is $10$ and the fifth term is $26$ . If the first term is $a_{1}$ , which is an equation for the $n$ th term of this sequence?

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Identify a sequence as explicit or recursive

Full solution

Q. Date:

\newline

Day

1

\newline

4

. F-IF.

1

.

3

\newline

Find the first five terms of the recursive sequence defined by the function below.

f(n)=2 f(n-1)+3 n

, where

f(1)=-2

\newline

5

. F-LE.

1

.

2

\newline

The third term in an arithmetic sequence is

10

and the fifth term is

26

. If the first term is

a_{1}

, which is an equation for the

n

th term of this sequence?

Calculate $f(3)$ : Now, let's find $f(3)$ .
$f(3) = 2f(3-1) + 3\times3$
$f(3) = 2f(2) + 9$
$f(3) = 2\times2 + 9$
$f(3) = 4 + 9$
$f(3) = 13$
Calculate $f(4)$ : Next, we calculate $f(4)$ .
$f(4) = 2f(4-1) + 3\times4$
$f(4) = 2f(3) + 12$
$f(4) = 2\times13 + 12$
$f(4) = 26 + 12$
$f(4) = 38$
Calculate $f(5)$ : Finally, we find $f(5)$ . $\newline$ $f(5) = 2f(5-1) + 3 \times 5$ $\newline$ $f(5) = 2f(4) + 15$ $\newline$ $f(5) = 2 \times 38 + 15$ $\newline$ $f(5) = 76 + 15$ $\newline$ $f(5) = 91$
Write nth term: Now we can write the nth term of the arithmetic sequence. $\newline$ The nth term $a_n = a_1 + (n - 1)d$ $\newline$ Since we know $d = 8$ , we substitute it into the equation. $\newline$ $a_n = a_1 + (n - 1)\times 8$
Find $a_{1}$ : To find $a_{1}$ , we use the third term which is $10$ . $\newline$ $10 = a_{1} + (3 - 1)\cdot8$ $\newline$ $10 = a_{1} + 2\cdot8$ $\newline$ $10 = a_{1} + 16$ $\newline$ $a_{1} = 10 - 16$ $\newline$ $a_{1} = -6$

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