find the sum of the first 20 terms of an a.p. whose nth term is given by an = An+B
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Question:
Find the sum of the first 20 terms of an a.p. whose nth term is given by an = An+B
Solution:
The sum of first 20 terms of the given sequence is 210A + 20B
Given :
- nth term , an= An + B………….(1)
On putting n = 1 in eq 1,
- a1 = A + B
On putting n = 20 in eq 1,
- a20 = A × 20 + B
- a20 = 20A + B
- a20 = l (last term) = 20A + B
By using the formula ,Sum of nth terms,
- Sn = n/2 [a + l]
→ S20 = 20/2 [a + l]
→ S20 = 10 [A + B + 20A + B]
→ S20 = 10 [21A + 2B]
→ S20 = 210A + 20B
Hence,
The sum of first 20 terms of the given sequence is 210A + 20B
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Answer:
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Step-by-step explanation:
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