Math help with sum of infinite geometric series please?

Question

Please show work so I can use for other question, thanks!

1) The sum of an infinite geometric series is 5/9 and the common ratio is -4/5. Find the first term

Answer 1

The sum of an infinite geometric series is S(infinite) = 5/9

The common ratio is r = -4/5

Find the first term a = ?

[Formula : The sum of an infinite geometric series is S(infinite) = [a / (1 - r)]

S(infinite)=5/9 and r=-4/5 value substitute above formula

5/9 = a / (1 - (-4/5))

Note : [ - * - = + ] ( Multiply two negative sign are positive)

5/9 = a / ( 1+ ( 4/5 ))

5/9 = a / ( (5+4)/5 )              here LCM in 1 , 5 is 5

5/9 = a / ( 9/5 )

Multiply each side by '9/5'.

( 5/9 )( 9/5 ) = [a / ( 9/5 )] ( 9/5)

Simplfy

1 = a

There fore

The first term a is 1