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Class 10 › Mathematics › Arithmetic Progressions
CBSE2026Class Class 10 · Mathematics1 Marks · Mcq✅ Verified
If sum of first ten terms of an A.P. is zero with $a$ as the first term and $d$, the common difference, which of the following relation is true?
A. $10a+9d=0$
B. $2a=9d$
C. $a_{10}=-a$
D. $a_{10}=a$
✅ Answer & Solution
✅ Correct Answer: C
Step 1: $$S_{10}=\frac{10}{2}\left[2a+(10-1)d\right]=5(2a+9d)$$
Step 2: Given $S_{10}=0$, so $2a+9d=0$, i.e. $9d=-2a$.
Step 3: The 10th term is $a_{10}=a+9d$.
Step 4: Substituting $9d=-2a$: $$a_{10}=a+(-2a)=-a$$
Step 5: Option (A) $10a+9d=0$ is wrong, and (B) has the wrong sign.
Answer: (C) $a_{10}=-a$
