Question

In the arithmetic sequence given below, what term is the number -45 7 5,(10)/(3),(5)/(3),ldots n= square

In the arithmetic sequence given below, what term is the number -45 7 5,(10)/(3),(5)/(3),ldots n= square
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Solution

Julia Coleman
Julia Coleman
Veteran · Tutor for 9 years

Answer

$n = 31$

Explanation

1. Identify the first term and common difference<br /> First term $a = 5$. Common difference $d = \frac{10}{3} - 5 = \frac{10}{3} - \frac{15}{3} = -\frac{5}{3}$.<br />2. Use the formula for the nth term of an arithmetic sequence<br /> The nth term is given by **$a_n = a + (n-1) \cdot d$**.<br />3. Set up the equation for the nth term equal to -45<br /> $-45 = 5 + (n-1) \cdot \left(-\frac{5}{3}\right)$.<br />4. Solve for n<br /> Simplify: $-45 = 5 - \frac{5}{3}(n-1)$.<br /> Subtract 5 from both sides: $-50 = -\frac{5}{3}(n-1)$.<br /> Multiply both sides by $-\frac{3}{5}$: $30 = n-1$.<br /> Add 1 to both sides: $n = 31$.
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