To complete the given series 138972, 150083, 161194, let's follow these steps:
1. Identify the given series:
[tex]\[
138972, 150083, 161194
\][/tex]
2. Calculate the differences between consecutive terms:
[tex]\[
150083 - 138972 = 11111
\][/tex]
[tex]\[
161194 - 150083 = 11111
\][/tex]
3. Observe that the differences are consistently the same:
The difference between the consecutive terms is 11111.
4. Use this common difference to find the next term in the series:
To find the next term, add the common difference to the last term in the series:
[tex]\[
161194 + 11111 = 172305
\][/tex]
Therefore, the complete series with the next term included is:
[tex]\[
138972, 150083, 161194, 172305
\][/tex]
