For number sequences formulas:A. Common difference: nth term = a + (n - 1)d d is difference between the numbers a is first term n is the nth term - leave it there.a = 5Eg formula for this number pattern: 5, 8, 11, 14, 17, 20... d = 3 therefore, formula is: 5 + (n - 1)(3) simplify ---> 5 + 3n - 3 = 2 + 3n (ans)B. Changing difference:nth term = a + (n - 1)d + ½(n - 1)(n - 2)ca is first term d is first difference c is difference of the difference n is the nth term - leave it thereEg Formula for this number pattern: 6, 8, 12, 18, 26...difference between each subsequent number is 2, 4, 6, 8... a = 6 d = 2 c = 2 therefore, formula is: 6 + (2)(n-1) + 2/2(n - 1)(n - 2)Simplify ---> 6 + 2n - 2 + 1( n2n - n + 2)^{2} - = 6 + 2n - 2 + n 2n ^{2} -- n + 2= 6 - n + n(ans)^{2 }^{(test the answers yourself!)
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Elementary Math >