Question

Write the first five terms of each of the following sequences whose $n$th terms are:$a_n=2n^2-3n+1$

Answer 1

$a_n=2n^2-3n+1...................eq\left(1\right)$

1) To find the first term of sequence $\left(a_1\right)$ put n=1 in eq(1)

$⟹a_1=2\times 1^2-3\times 1+1$

$⟹a_1=2-3+1$

$⟹a_1=0$

2) To find the second term of sequence $\left(a_2\right)$ put n=2 in eq(1)

$⟹a_2=2\times 2^2-3\times 2+1$

$⟹a_2=8-6+1$

$⟹a_2=3$

3) To find the third term of sequence $\left(a_3\right)$ put n=3 in eq(1)

$⟹a_3=2\times 3^2-3\times 3+1$

$⟹a_3=18-9+1$

$⟹a_3=10$

4) To find the fourth term of sequence $\left(a_4\right)$ put n=4 in eq(1)

$⟹a_4=2\times 4^2-3\times 4+1$

$⟹a_4=32-12+1$

$⟹a_4=21$

5) To find the fifth term of sequence $\left(a_5\right)$ put n=5 in eq(1)

$⟹a_5=2\times 5^2-3\times 5+1$

$⟹a_5=50-15+1$

$⟹a_5=36$