NumericalModerate1.5 marks
4(ii)
The first term of an Arithmetic Progression (A.P.) is 5, the last term is 50 and their sum is 440. Find:
the number of terms
Topic: Arithmetic progression
Previous-year question practice database
Answer
Exam answer
Given:
First term a = 5 Last term l = 50 Sum Sₙ = 440
Let the number of terms be n.
Formula for the sum of an Arithmetic Progression:
Sₙ = n/2 (a + l)
Substitute the given values:
440 = n/2 (5 + 50)
440 = n/2 × 55
440 = 55n/2
440 × 2 = 55n
880 = 55n
n = 880/55
n = 16
Answer:
Number of terms = 16.
Explanation
The sum formula Sₙ = n/2(a+l) is used because the first term, last term and total sum are given.