Question

find the sequence if Tn =2n-1

Answer 1

solution:

Given:$T_n=2n-1$

To find:sequence($a_1,a_2,...$)

$T_n$=sum of series from 1 to n (similar to$S_n$

if n=1then,$T_1=a_1=a$
$T_n=2n-1$
$T_1=2(1)-1$
$T_1=2-1$
$T_1=1$  ∴$a_1=1$

if n=2 then,$T_2=a_1+a_2$
$T_2=2(2)-1$
$T_2=4-1$
$T_2=3$

as  $T_2=a_1+a_2$
$3=1+a_2$
3=1+a+(2-1)d
3=1+1+(1)d
3=2+d
∴d=1

As we know that $a_n=a+(n-1)d$

$a_2=a+(2-1)d$
$a_2=1+(1)1$
$a_2=1+1$
$a_2=2$

[tex]a_3=a+(3-1)d [/tex]
$a_3=1+(2)1$
$a_3=1+2$
$a_3=3$

And hence,the sequence is 1,2,3..

Answer 2

T1 =2*1-1.=1
T2=2*2-1=3
T3=2*3-1=5
T4=2*4-1=7
Therefore answer was 1,3,5,7,9,11 . . . . .