The series is a(n) = 4n² +5n. . . and this is the general formula which also gives the nth term.
When n = 1, 4n² + 5n = 4*1 + 5*1 = 9
When n = 2, 4n² + 5n = 4*4 + 5*2 = 26 . . .and so on
When n = 5, 4n² + 5n = 4*25 + 5*5 = 125.
The series can be determined using the Difference Technique.
A second difference of 8 gives the first term 4n². . . . as a 2nd difference of 2 equates to n².
After applying this to the original series, the revised series produces a 1st difference of 5, hence 5n.
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The given sequence is 11, 31, 51, 72 The nth term of this sequence can be expressed as an = 11 + (n - 1) × 20 Therefore, the nth term is 11 + (n - 1) × 20, where n is the position of the term in the sequence.
If by using the formula: nth term = n2+2 the sequence is 3 6 11 18 27 38 51 66.Then it follows that by using the same formula the sequence is III VI XI XVIII XXVII XXXVIII LI LXVI in Roman numerals.
125%
To convert a decimal to a fractionm. Place the decimal over 'one point' followed by the same number of zeroes as digits in the decimal number. Hence 0.408 / 1.000 Cancel down the decimal point 0408 / 1000 Drop the trivial zero to the left of 408 Hence 408/1000 Cancel down by '4' 102/ 250 Cancel down by '2' 51/125 This will not cancel down any further as there are no common factors between '51' and '125'. Hence 0.408 = 51/125
The ordinal number for 26 is twenty sixth of 26th and that of 51 is fifty first of 51st.