In an AP, (S_{12}=438) and (S_{24}=1596). Find the value of (S_{36}).
Answer and explanation
Correct answer: (3474)
For an arithmetic progression with first term a and common difference d, the sum formula is \\(S_n=\frac{n}{2}[2a+(n-1)d]\\). Using \\(S_{12}=438\\) gives \\(2a+11d=73\\), and using \\(S_{24}=1596\\) gives \\(2a+23d=133\\). Subtracting these equations gives \\(12d=60\\), so \\(d=5\\). Then \\(2a+55=73\\), hence \\(a=9\\).
Now apply the same formula at n=36: \\(S_{36}=\frac{36}{2}[2(9)+35(5)]\\=18(18+175)=18(193)=3474\\). Therefore option A is correct. The important step is to determine the progression from the two given partial sums before calculating the requested sum.
Frequently asked questions
What is the correct answer to this question?
(3474)
Why is this the correct answer?
For an arithmetic progression with first term a and common difference d, the sum formula is \\(S_n=\frac{n}{2}[2a+(n-1)d]\\). Using \\(S_{12}=438\\) gives \\(2a+11d=73\\), and using \\(S_{24}=1596\\) gives \\(2a+23d=133\\). Subtracting these equations gives \\(12d=60\\), so \\(d=5\\). Then \\(2a+55=73\\), hence \\(a=9\\).
Now apply the same formula at n=36: \\(S_{36}=\frac{36}{2}[2(9)+35(5)]\\=18(18+175)=18(193)=3474\\). Therefore option A is correct. The important step is to determine the progression from the two given partial sums before calculating the requested sum.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the sum of the first $n$ terms of an AP.
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