Question

Find the 100th AND the nth term for the following sequence. Please show work.

a. 197+7 x 3^27, 197+8 x 3^27, 197+9 x 3^27

Answer 1

Answer:

The 100th term is $a_{100}=197+106.3^{27}$

The nth term is $a_n=197+(n+6).3^{27}$

Step-by-step explanation:

Forming the sequence we see that

$a_1=197+7.3^{27}=197+(1+6).3^{27}$

$a_2=197+8.3^{27}=197+(2+6).3^{27}$

$a_3=197+9.3^{27}=197+(3+6).3^{27}$

Evidently,

$a_n=197+(n+6).3^{27}$

So,

$a_{100}=197+106.3^{27}$