What will be the 24th term of the AP 18, 22, 26, 30, ...?
Answer and explanation
Correct answer: 110
For an arithmetic progression, the nth term is given by aₙ = a + (n − 1)d. Here a = 18 and d = 22 − 18 = 4. Substituting n = 24 gives a₂₄ = 18 + (24 − 1)×4 = 18 + 23×4 = 18 + 92 = 110. Therefore option B is correct. The multiplier is 23 because the first term is counted as the starting value and only 23 equal increases are needed to reach the 24th term. Option A results from using too few increments, option C from using one extra increment, and option D does not reflect the sequence's steady increase. The answer can also be checked by adding 4 successively from the first term.
Frequently asked questions
What is the correct answer to this question?
110
Why is this the correct answer?
For an arithmetic progression, the nth term is given by aₙ = a + (n − 1)d. Here a = 18 and d = 22 − 18 = 4. Substituting n = 24 gives a₂₄ = 18 + (24 − 1)×4 = 18 + 23×4 = 18 + 92 = 110. Therefore option B is correct. The multiplier is 23 because the first term is counted as the starting value and only 23 equal increases are needed to reach the 24th term. Option A results from using too few increments, option C from using one extra increment, and option D does not reflect the sequence's steady increase. The answer can also be checked by adding 4 successively from the first term.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
