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The concept of Figurate numbers is very ancient but it continues to fascinate amateur and professional mathematicians to this day. The connection between the two oldest branches of mathematics namely number theory and geometry was made possible in the study of Figurate numbers. In this paper, after introducing Figurate numbers formally, we had defined a new concept which is identified as Cesaro – Like summation and apply it for the family of Figurate numbers in two kinds. These ideas will pave a new way for deep understanding and further generalizations in summability theory.