Which term describes a slowdown in the rate of increase in the consumer price index?

Disinflation

Explanation:

Consumer price index expresses the general price level of consumer goods and services in an economy.

When the general price level of goods and services goes up (in an economy), such an economy is said to be experiencing inflation.

If the prices keep rising, inflation is said to persist. But when the rate of increase in general price level begins to slow down, a form of the opposite of inflation called disinflation (not to be confused with deflation) is used to describe this general slowing down in the increase of general price level.

If the initial rate of inflation isn't that great, disinflation can lead to deflation (deflation is the general decrease in general price level of goods and services in an economy; the direct opposite of inflation!)