The sum of first n terms of an arithmetic series is 216. The value of the first term is n and the value of the nth term is 2n. The common difference d is:
Given:
Sum of first n terms, S = 216
First term, a = n
nth term, l = 2n
Using the sum formula of an AP:
S = n/2 × (a + l)
216 = n/2 × (n + 2n)
216 = n/2 × 3n
216 = 3n²/2
n² = 144
n = 12
Now use the nth term formula:
l = a + (n − 1)d
24 = 12 + 11d
11d = 12
d = 12/11
Answer = 12/11 ✅
Important Questions from Arithmetic Progressions
What is \(\displaystyle \sum_{n=1}^{34} a_n\) equal to ?
The first and the second terms of an AP are \(\frac{5}{2}\) and \(\frac{23}{12}\) respectively. If nth term is the largest negative term, what is the value of n ?
In an AP, the first term is x and the sum of the first n terms is zero. What is the sum of next m terms ?
p, q, r and s are in AP such that p + s = 8 and qr = 15. What is the difference between largest and smallest numbers ?
The arithmetic mean of 1, 8, 27, 64, … up to n terms is given by
