The sum of the first 3 terms of a geometric series is 171 and the common ratio is 2/3
What is the first term of the series?

Work Shown:

a = first term

a*(2/3) = (2/3)a= second term

(2/3)a*(2/3) = (4/9)a = third term

note how I multiplied each previous term by the common ratio (2/3) to get the next term

Add up the three terms

a + (2/3)a + (4/9)a = (9/9)a + (6/9)a + (4/9)a = (19/9)a

Set this equal to 171, which is what we want the first three terms to sum to, then solve for 'a'

(19/9)a = 171

a = (9/19)*171

a = 81 is the first term

Checking the

a = 81 = first term

(2/3)*a = (2/3)*81 = 54 = second term

(4/9)*a = (4/9)*81 = 36 = third term

adding up the three terms gets us

81+54+36 = 171

so we have confirmed the answer

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