Question
Write the sequence with $n^{th}$ term:
$a_n = 5 + 2n.$
Show the all of the above sequences form A.P.
$a_n = 5 + 2n.$
Show the all of the above sequences form A.P.
✓
Answer
$a_n = 5 + 2n$
Put $n = 1, 2, 3...$
$a_1 = 5 + 2 \times 1 = 7$
$a_2 = 5 + 2 \times 2 = 9$
$a_3 = 5 + 2 \times 3 = 11$
$a_2 - a_1 = a_3 - a_2$
$9 - 7 = 11 - 9$
$2 = 2$
Common difference is $2$
So that
A.P, $7, 9, 11, 13, 15...$
Put $n = 1, 2, 3...$
$a_1 = 5 + 2 \times 1 = 7$
$a_2 = 5 + 2 \times 2 = 9$
$a_3 = 5 + 2 \times 3 = 11$
$a_2 - a_1 = a_3 - a_2$
$9 - 7 = 11 - 9$
$2 = 2$
Common difference is $2$
So that
A.P, $7, 9, 11, 13, 15...$
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