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
$a_1 = 1, a_n - a_{n-1} + 2$
Let $n = 2, 3, 4, 5, 6$
$\therefore$ $a_2 = a_{2-1} + 2 = a_1 + 2$
$= 1 + 2 = 3$ ($\because$ $a_1 = 1$)
$a_3 = a_{3-1} + 2 = a_2 + 2$
$= 3 + 2 = 5$
$a_4 = a_{4-1} + 2 = a_3 + 2$
$= 5 + 2 = 7$
$a_5 = a_{5-1} + 2 = a_4 + 2$
$= 7 + 2 = 9$
$a_6 = a_{6-1} + 2 = a_5 + 2$
$= 9 + 2 = 11.$
Let $n = 2, 3, 4, 5, 6$
$\therefore$ $a_2 = a_{2-1} + 2 = a_1 + 2$
$= 1 + 2 = 3$ ($\because$ $a_1 = 1$)
$a_3 = a_{3-1} + 2 = a_2 + 2$
$= 3 + 2 = 5$
$a_4 = a_{4-1} + 2 = a_3 + 2$
$= 5 + 2 = 7$
$a_5 = a_{5-1} + 2 = a_4 + 2$
$= 7 + 2 = 9$
$a_6 = a_{6-1} + 2 = a_5 + 2$
$= 9 + 2 = 11.$
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