(i) Find a formula for the sum S of any four consecutive odd numbers. (ii) Hence, find the value of S when the greatest odd number is -17 .

Define Odd Numbers: Let's denote the first odd number as n. Since odd numbers are 2 units apart, the next three consecutive odd numbers would be n+2, n+4, and n+6.Calculate Sum Formula: To find the formula for the sum S of these four consecutive odd numbers, we add them together: S = n + (n+2) + (n+4) + (n+6).Simplify Formula: Simplify the formula by combining like terms: S = 4n + 12.Find Value of n: Now, we need to find the value of S when the greatest odd number is -17. Since the greatest number in our sequence is n+6, we set n+6 = -17.Solve for n: Solve for n: n = -17 - 6.Calculate n: Calculate n: n = -23.Substitute n into Formula: Now that we have the value of n, we can find S by substituting n into our formula S = 4n + 12.Calculate S: Calculate S: S = 4(-23) + 12.Simplify Calculation: Simplify the calculation: S = -92 + 12.Final Calculation: Final calculation for S: S = -80.

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(i) Find a formula for the sum
S of any four consecutive odd numbers.
(ii) Hence, find the value of
S when the greatest odd number is -17 .

(i) Find a formula for the sum $S$ of any four consecutive odd numbers. $\newline$ (ii) Hence, find the value of $S$ when the greatest odd number is $-17$ .

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Algebra 1

Consecutive integer problems

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Q. (i) Find a formula for the sum

S

of any four consecutive odd numbers.

\newline

(ii) Hence, find the value of

S

when the greatest odd number is

-17

Define Odd Numbers: Let's denote the first odd number as $n$ . Since odd numbers are $2$ units apart, the next three consecutive odd numbers would be $n+2$ , $n+4$ , and $n+6$ .
Calculate Sum Formula: To find the formula for the sum $S$ of these four consecutive odd numbers, we add them together: $S = n + (n+2) + (n+4) + (n+6)$ .
Simplify Formula: Simplify the formula by combining like terms: $S = 4n + 12$ .
Find Value of n: Now, we need to find the value of $S$ when the greatest odd number is $-17$ . Since the greatest number in our sequence is $n+6$ , we set $n+6 = -17$ .
Solve for n: Solve for n: $n = -17 - 6$ .
Calculate n: Calculate $n$ : $n = -23$ .
Substitute $n$ into Formula: Now that we have the value of $n$ , we can find $S$ by substituting $n$ into our formula $S = 4n + 12$ .
Calculate S: Calculate S: $S = 4(-23) + 12$ .
Simplify Calculation: Simplify the calculation: $S = -92 + 12$ .
Final Calculation: Final calculation for $S$ : $S = -80$ .