Class 11

Math

Co-ordinate Geometry

Straight Lines

Write the first five terms of each of the following sequences whose $n$th terms are: $a_{n}=2n(n−2) $

$a_{n}=2n(n−2) ...................eq(1)$

1) To find the first term of sequence $(a_{1})$ put n=1 in eq(1)

$⟹a_{1}=21(1−2) $

$⟹a_{1}=21(−1) $

$⟹a_{1}=−21 $

2) To find the second term of sequence $(a_{2})$ put n=2 in eq(1)

$⟹a_{2}=22(2−2) $

$⟹a_{2}=22(0) $

$⟹a_{2}=20 $

$⟹a_{2}=0$

3) To find the third term of sequence $(a_{3})$ put n=3 in eq(1)

$⟹a_{3}=23(3−2) $

$⟹a_{3}=23(1) $

$⟹a_{3}=23 $

4) To find the fourth term of sequence $(a_{4})$ put n=4 in eq(1)

$⟹a_{4}=24(4−2) $

$⟹a_{4}=24(2) $

$⟹a_{4}=28 $

$⟹a_{4}=4$

5) To find the fifth term of sequence $(a_{5})$ put n=5 in eq(1)

$⟹a_{5}=25(5−2) $

$⟹a_{5}=25(3) $

$⟹a_{5}=215 $