Question
Find the next five terms of the following sequences given:
$\text{a}_1=-1,\text{a}_\text{n}=\frac{\text{a}_\text{n}-1}{\text{n}},\text{n}\geq2$
$\text{a}_1=-1,\text{a}_\text{n}=\frac{\text{a}_\text{n}-1}{\text{n}},\text{n}\geq2$
✓
Answer
Given, first term $(a_1) = -1$
$n^{th}$ term $(a_n)$ $=\frac{\text{a}_\text{n}-1}{\text{n}},\text{n}\geq2$
To find next five terms i.e., $a_2, a_3, a_4, a_5, a_6$ we put $n = 2, 3, 4, 5, 6$ is an
$\text{a}_2=\frac{\text{a}_{2-1}}{2}=\frac{\text{a}_1}{2}=\frac{-1}{2}$
$\text{a}_3=\frac{\text{a}_{3-1}}{3}=\frac{\text{a}_2}{3}=\frac{-\frac{1}{2}}{3}=\frac{-1}{6}$
$\text{a}_4=\frac{\text{a}_{4-1}}{4}=\frac{\text{a}_3}{4}=\frac{\frac{-1}{6}}{4}=\frac{-1}{24}$
$\text{a}_5=\frac{\text{a}_{5-1}}{5}=\frac{\text{a}_4}{5}=\frac{\frac{-1}{24}}{5}=\frac{-1}{120}$
$\therefore$ The next five terms are,
$\text{a}_2=\frac{-1}{2},\text{a}_3=\frac{-1}{6},\text{a}_4=\frac{-1}{24},\text{a}_5=\frac{-1}{120},\text{a}_6=\frac{-1}{720}$
$n^{th}$ term $(a_n)$ $=\frac{\text{a}_\text{n}-1}{\text{n}},\text{n}\geq2$
To find next five terms i.e., $a_2, a_3, a_4, a_5, a_6$ we put $n = 2, 3, 4, 5, 6$ is an
$\text{a}_2=\frac{\text{a}_{2-1}}{2}=\frac{\text{a}_1}{2}=\frac{-1}{2}$
$\text{a}_3=\frac{\text{a}_{3-1}}{3}=\frac{\text{a}_2}{3}=\frac{-\frac{1}{2}}{3}=\frac{-1}{6}$
$\text{a}_4=\frac{\text{a}_{4-1}}{4}=\frac{\text{a}_3}{4}=\frac{\frac{-1}{6}}{4}=\frac{-1}{24}$
$\text{a}_5=\frac{\text{a}_{5-1}}{5}=\frac{\text{a}_4}{5}=\frac{\frac{-1}{24}}{5}=\frac{-1}{120}$
$\therefore$ The next five terms are,
$\text{a}_2=\frac{-1}{2},\text{a}_3=\frac{-1}{6},\text{a}_4=\frac{-1}{24},\text{a}_5=\frac{-1}{120},\text{a}_6=\frac{-1}{720}$
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