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:
The sequence of numbers where the difference of any two consecutive terms is same is called an Arithmetic Progression.
If a be the first term, d be the common difference and n be the number of terms of an AP, then the sequence can be written as follows: a,a+d,a+2d,...,a+(n−1)d
The sum of n terms of the above series is given by: Sn=‌
n
2
[a+{a+(n−1)d}]=(‌
‌ First Term ‌+‌ Last Term ‌
2
)×n
Calculation: Let's say that the first term of the AP is a and the common difference is d. According to the question, the first term is n, the n‌th ‌ term (Last Term) is 2n and the sum of the first n terms (Sn) is 216 . Using Sn=(‌
‌ First Term ‌+‌ Last Term ‌
2
)×n, we get : ⇒216=(‌
n+2n
2
)×n ⇒n2=‌
216×2
3
=144 ⇒n=12 Now using an=a+(n−1)d, we get: =2n=n+(n−1)d ⇒d=‌