Write the first five terms of the sequence wh | vedclass

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(A) To find the first five terms,we substitute $n = 1, 2, 3, 4, 5$ into the formula $a_{n} = n \frac{n^{2}+5}{4}$.For $n=1$: $a_{1} = 1 \cdot \frac{1^

Vedclass · Accepted Answer

$\frac{3}{2}, \frac{9}{2}, \frac{21}{2}, 21, \frac{75}{2}$

Vedclass · Answer

(A) To find the first five terms,we substitute $n = 1, 2, 3, 4, 5$ into the formula $a_{n} = n \frac{n^{2}+5}{4}$.For $n=1$: $a_{1} = 1 \cdot \frac{1^{2}+5}{4} = \frac{6}{4} = \frac{3}{2}$.For $n=2$: $a_{2} = 2 \cdot \frac{2^{2}+5}{4} = 2 \cdot \frac{9}{4} = \frac{9}{2}$.For $n=3$: $a_{3} = 3 \cdot \frac{3^{2}+5}{4} = 3 \cdot \frac{14}{4} = \frac{42}{4} = \frac{21}{2}$.For $n=4$: $a_{4} = 4 \cdot \frac{4^{2}+5}{4} = 4 \cdot \frac{21}{4} = 21$.For $n=5$: $a_{5} = 5 \cdot \frac{5^{2}+5}{4} = 5 \cdot \frac{30}{4} = \frac{150}{4} = \frac{75}{2}$.Thus,the first five terms are $\frac{3}{2}, \frac{9}{2}, \frac{21}{2}, 21, \frac{75}{2}$.

Write the first five terms of the sequence whose $n^{th}$ term is $a_{n} = n \frac{n^{2}+5}{4}$.

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