The average of a set of 18 consecutive integers is 22.5. What is the largest integer in the set?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 31.
We know that,
Sum of n terms of an AP = n(a + l)/2 ---- (1)
Where, a = first term and l = last term
If the first term is a then, the last term i.e. 18th term = a + 17
Using equation (1), we get
Sum of 18 terms = 18 × (a + a + 17)/2
Average of 18 terms = [18 × (2a + 17)/2]/18
Average = (2a + 17)/2
⇒ (2a + 17)/2 = 22.5
⇒ 2a + 17 = 45
⇒ 2a = 28
⇒ a = 14
Hence, the largest number = a + 17 = 14 + 17 = 31