Question
Write the first five terms of the following sequences whose $n^{th}$ terms are:
$a_n = 2n^2 - 3n + 1.$
$a_n = 2n^2 - 3n + 1.$
✓
Answer
$a_n = 2n^2 - 3n + 1$.The given sequence is $a_n = 2n^2 - 3n + 1$.
To write first tive terms of given sequence an, we put $n = 1, 2, 3, 4, 5$. Then we get
$a_1 = 2.1^2 - 3.1 + 1 = 2 - 3 + 1 = 0$
$a_2 = 2.2^2 - 3.2 + 1 = 8 - 6 + 1 = 3$
$a_3 = 2.3^2 - 3.3 + 1 = 18 - 9 + 1 = 10$
$a_4 = 2.4^2 - 3.4 + 1 = 32 - 12 + 1 = 21$
$a_5 = 2.5^2 - 3.5 + 1 = 50 - 15 + 1 = 36$
$\therefore$ The required first five tms of given sequence $a_n = 2n^2 - 3n + 1$ are $0, 3, 10, 21, 36.$
To write first tive terms of given sequence an, we put $n = 1, 2, 3, 4, 5$. Then we get
$a_1 = 2.1^2 - 3.1 + 1 = 2 - 3 + 1 = 0$
$a_2 = 2.2^2 - 3.2 + 1 = 8 - 6 + 1 = 3$
$a_3 = 2.3^2 - 3.3 + 1 = 18 - 9 + 1 = 10$
$a_4 = 2.4^2 - 3.4 + 1 = 32 - 12 + 1 = 21$
$a_5 = 2.5^2 - 3.5 + 1 = 50 - 15 + 1 = 36$
$\therefore$ The required first five tms of given sequence $a_n = 2n^2 - 3n + 1$ are $0, 3, 10, 21, 36.$
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