Solving Arithmetic Series Problems

What is the formula used to calculate the sum of an arithmetic series?

• S = n/2 [a + (n-1)d]

• S = n [a + (n-1)d]

• S = n/2 [2a + (n-1)d]

• S = n [2a + (n-1)d]

What is the importance of writing down the formula accurately?

• To memorize it for future use

• To save time during the exam

• To ensure correct substitution and calculation

• To impress the examiner

If the sum of the first 48 terms is four times the sum of the first 36 terms, what is the relationship between these sums?

• S48 = S36 - 4

• S48 = S36 + 4

• S48 = S36 / 4

• S48 = 4 * S36

What is the simplified expression for the sum of the first 36 terms in terms of X?

• 18 [2a + 35d] = X

• 36 [2a + 35d] = X

• 18 [2a + 47d] = X

• 36 [2a + 47d] = X

How do you express 'a' in terms of 'D' after solving the equations?

• a = 24D

• a = -14.5D

• a = 14.5D

• a = -24D

What is the sum of the first 30 terms of the series?

• 30

• 45

• 15

• 0

What was the first mark awarded for in the question breakdown?

• Correct substitution into the formula

• Correct expression in terms of X

• Correct value of 'a'

• Correct final answer

What was the final answer for the sum of the first 30 terms?

• 45

• 30

• 15

• 0

What is the significance of the brackets canceling out in the final calculation?

• It results in a sum of 45

• It results in a sum of 30

• It results in a sum of 15

• It results in a sum of 0

What was the fourth mark awarded for in the question breakdown?

• Correct value of 'a'

• Correct expression in terms of X

• Correct final answer

• Correct substitution into the formula