Every whole number with a units digit of 5 can be represented by the expression 10x + 5, where x is a whole number. For example, 35 = 10(3) + 5 and 145 = 10(14) + 5. Now let’s observe the following pattern when squaring such a number.(10x + 5)2 = 100x2 + 100x + 25                 = 100x(x + 1) + 25 The pattern inside the dashed box can be stated as “add 25 to the product of x, x + 1, and 100.” Thus, to compute 352 mentally, we can figure “352 = 3(4)(100) + 25 = 1225.” Compute each of the following numbers mentally, and then check your answers.(a) 152   (b) 252   (c) 452(d) 552   (e) 652   (f ) 752(g) 852   (h) 952   (i) 1052

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.