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If the sum of the first 9 terms of an AP is equal to sum of e •first 11 terms, then what is the sum of the first 20 terms?
20
10
2
0
- We start with the formula for the sum of n terms of an arithmetic progression (AP): Sn=n2×(2a+(n−1)d), where a is the first term and d is the common difference.
- According to the question, the sum of the first 9 terms is equal to the sum of the first 11 terms:
S9=S11
This implies:
92×(2a+8d)=112×(2a+10d)
- Simplifying this equation, we get:
9(2a+8d)=11(2a+10d)
18a+72d=22a+110d
Rearranging gives:
4a+38d=0
- Solving for a, we find:a=−384d
- Then, to find the sum of the first 20 terms:
S20=202×(2a+19d)=10×(2×−384d+19d)=10×(19d−19d)=10×0=0
- Option 4: 0 is correct.
- .
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