Problem

(1) Write the algebraic expression for each of the sequences below: i) Sequence of odd numbers ii) Sequence of natural numbers which leave remainder 1 on division by 3 . iii) The sequence of natural numbers ending in 1 . iv) The sequence of natural numbers ending in 1 or 6 . 2) For the sequence of regular polygons starting with an equilateral triangle,

Solution

Step 1 :\(\text{i) Sequence of odd numbers: } 2n - 1\)

Step 2 :\(\text{ii) Sequence of natural numbers which leave remainder 1 on division by 3: } 3n - 2\)

Step 3 :\(\text{iii) The sequence of natural numbers ending in 1: } 10n + 1\)

Step 4 :\(\text{iv) The sequence of natural numbers ending in 1 or 6: } 5n + 1\)

Step 5 :\(\text{2) For the sequence of regular polygons starting with an equilateral triangle: }\)

Step 6 :\(\text{Number of sides: } n + 2\)

Step 7 :\(\text{Sum of interior angles: } 180(n - 2)\)

Step 8 :\(\text{Each interior angle: } \frac{180(n - 2)}{n}\)

Step 9 :\(\boxed{\text{Final expressions:}}\)

Step 10 :\(\boxed{\text{i) } 2n - 1}\)

Step 11 :\(\boxed{\text{ii) } 3n - 2}\)

Step 12 :\(\boxed{\text{iii) } 10n + 1}\)

Step 13 :\(\boxed{\text{iv) } 5n + 1}\)

Step 14 :\(\boxed{\text{2) } \frac{180(n - 2)}{n}}\)

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