How do you find the seventeenth term in the arithmetic sequence for which a=4.5 and d=0.2?

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How do you find the seventeenth term in the arithmetic sequence for which a=4.5 and d=0.2?

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Answer 1 · 2016-02-01T17:47:11

seventeenth term $= 7.7$ $=7.7$

Explanation:

Recall the general term in an arithmetic sequence is written as:

$t_{n} = a + (n - 1) d$ $t_n=a+(n-1)d$

where:
$t_{n} =$ $t_n=$ term number
$a =$ $a=$ first term
$n =$ $n=$ number of terms
$d =$ $d=$ common difference

To solve for the seventeenth term, substitute your known values into the equation:

$t_{n} = a + (n - 1) d$ $t_n=a+(n-1)d$

$t_{17} = 4.5 + (17 - 1) (0.2)$ $t_17=4.5+(17-1)(0.2)$

$t_{17} = 4.5 + (16) (0.2)$ $t_17=4.5+(16)(0.2)$

$t_{17} = 4.5 + 3.2$ $t_17=4.5+3.2$

$t_{17} = 7.7$ $color(green)(t_17=7.7)$

Note that the seventeenth term is also $t_{17} = a + 16 d$ $t_17=a+16d$ . If you used this equation, it would produce the same answer:

$t_{17} = a + 16 d$ $t_17=a+16d$

$t_{17} = 4.5 + 16 (0.2)$ $t_17=4.5+16(0.2)$

$t_{17} = 4.5 + 3.2$ $t_17=4.5+3.2$

$t_{17} = 7.7$ $color(green)(t_17=7.7)$

$:.$ , the seventeenth term is $7.7$ .

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How do you find the seventeenth term in the arithmetic sequence for which a=4.5 and d=0.2?

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