The sum of all the terms in an infinite geometric sequence is 81 and the sum of all terms starting from the third is 9. What is the second term in the sequence?

Step (1)

We know that the sum of all the terms in an infinite geometric sequence finding from following equation whenever |q| < 1 .

q = magnitude

So :

Remember it I'll use it again.

_________________________________

Step (2)

We know that the sum of the n first terms of a geometric sequence finding from following equation.

_________________________________

Sum of all terms starting from the third is 9.

So :

Sides minus 9

So :

Factoring t(1)

We have found t(1) = 81 ( 1 - q ) in step (1).

So :

Divided sides by 81

Subtract sides minus -1

Negatives simplifies

Radical sides

_________________________________

Step (4)

If q = 1/3 :

So :

°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°

If q = - 1/3 :

So :

_________________________________

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

1

step-by-step explanation:

it's the only multiple of both and the least

i think is 3 and 6. this took me 10 min to think.hope to and hope that my answer is brainliest.(follow me )