Find first term in a geometric series
Calculator

The series of number pattern was assumed to behave in geometric series pattern

Step 1. Enter 2 in box n₂ Why? It is the second number in geometric series.

Step 2. Enter 0.3 decimal equivalent of 3/10 the recorded value for second number

Step 3. Enter 6 in box n₆

Step 4. Enter 1.51875 decimal equivalent of 243/160 the recorded value for the sixth number. Select Calculate

Step 5. The answer is letter a = the first term of geometric series

Step 6. Now you can enter any integer number in box n _nth to compute the expected value for any nth term

Step 7. Now play with the interactive graph shown below to predict the last term.

a = r = n2 = L2 = a =

nnth = Lnth = n6 = L6 = r =

The Graph of Geometric Function y = a r ^n-1

Notice the equation is similar to the Last Term equation L_n = a r ^n-1
Here a = first term of the series = 0.20 ;
r = geometric ratio = 1.5
And n = number of series is represented by the x-axis
While L = last term value is represented by the y-axis.
As you move the graph, the last term value (y-axis) can be predicted
for every value of "nth" term (x-axis) same result as the above calculator.