Question

Find the general term Tn for the following sequences;
a) 9; 14; 19
b) 3; 7; 11
c) 8; 15; 22
d) 4; 11; 18

Answer 1

$a) 9; 14; 19$

$a_1=9;a_2=14;a_3=19\implies$ $a_2-a_1=14-9=5$

$=a_3-a_2=19-14=5\implies d=5$ (Common Difference)

So,This is an $A.P.$

$T_n=a_1+(n-1)d=9+(n-1)5=4+5n$

$b) \ 3; 7; 11$

$a_1=3;a_2=7;a_3=11\implies$ $a_2-a_1=7-3=4$

$=a_3-a_2=11-7=4\implies d=4$

So,This is an Arithmetic progression.

$T_n=a_1+(n-1)d=3+(n-1)4=-1+4n$

$c)\ 8; 15; 22$

$a_1=8;a_2=15;a_3=22\implies$ $a_2-a_1=15-8=7$

$=a_3-a_2=22-15=7\implies d=7$

So,This is an Arithmetic progression.

$T_n=a_1+(n-1)d=8+(n-1)7=1+7n$

$d) \ 4; 11; 18$

$a_1=4;a_2=11;a_3=18\implies$ $a_2-a_1=11-4=7$

$=a_3-a_2=18-11=7\implies d=7$

So,This is an Arithmetic progression.

$T_n=a_1+(n-1)d=4+(n-1)7=-3+7n$