Question
Find the next five terms of the following sequences given:
$\text{a}_1=1,\text{a}_\text{n}=\text{a}_{\text{n}-1}+2,\text{n}\geq2.$
$\text{a}_1=1,\text{a}_\text{n}=\text{a}_{\text{n}-1}+2,\text{n}\geq2.$
✓
Answer
$ a_1=1, a_n-a_{n-1}+2$
$ \text { Let } n=2,3,4,5,6$
$ \therefore a_2=a_{2-1}+2=a_1+2$
$ =1+2=3\left(\because a_1=1\right)$
$ a_3=a_{3-1}+2=a_2+2$
$ =3+2=5$
$ a_4=a_{4-1}+2=a_3+2$
$ =5+2=7$
$ a_5=a_{5-1}+2=a_4+2$
$ =7+2=9$
$ a_6=a_{6-1}+2=a_5+2$
$ =9+2=11$
$ \text { Let } n=2,3,4,5,6$
$ \therefore a_2=a_{2-1}+2=a_1+2$
$ =1+2=3\left(\because a_1=1\right)$
$ a_3=a_{3-1}+2=a_2+2$
$ =3+2=5$
$ a_4=a_{4-1}+2=a_3+2$
$ =5+2=7$
$ a_5=a_{5-1}+2=a_4+2$
$ =7+2=9$
$ a_6=a_{6-1}+2=a_5+2$
$ =9+2=11$
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