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Find the 11th term of the geometric semence. 3,-3,3,ldots

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Find the 11th term of the geometric semence.
3,-3,3,ldots

Find the 11th term of the geometric semence. 3,-3,3,ldots

Solução

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EmíliaElite · Tutor por 8 anos

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To find the term of the geometric sequence $3, -3, 3, \ldots$, we need to identify the common ratio between consecutive terms.<br /><br />The common ratio (r) can be found by dividing any term by its previous term. Let's calculate the common ratio using the first two terms:<br /><br />$r = \frac{-3}{3} = -1$<br /><br />Now that we have the common ratio, we can use the formula for the nth term of a geometric sequence:<br /><br />$a_n = a_1 \cdot r^{(n-1)}$<br /><br />where $a_n$ is the nth term, $a_1$ is the first term, and n is the term number.<br /><br />In this case, $a_1 = 3$, $r = -1$, and $n = 11$. Plugging these values into the formula, we get:<br /><br />$a_{11} = 3 \cdot (-1)^{(11-1)}$<br /><br />$a_{11} = 3 \cdot (-1)^{10}$<br /><br />Since any number raised to an even power is positive, we have:<br /><br />$a_{11} = 3 \cdot 1$<br /><br />$a_{11} = 3$<br /><br />Therefore, the 11th term of the geometric sequence $3, -3, 3, \ldots$ is 3.
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