Consider the following statements  I. If an denotes  the  nth  term  of an AP, then  an=an+k+an−k2   II. In an  AP, if the Sum  of m  terms  is equal to the sum of n terms, then the sum of(m  + n)  terms is always  zero. Which of the  statement is given  above is/are correct?

# Consider the following statements  denotes  the  nth  term  of an AP, then  ${\mathrm{a}}_{\mathrm{n}}=\frac{{\mathrm{a}}_{\mathrm{n}+\mathrm{k}}+{\mathrm{a}}_{\mathrm{n}-\mathrm{k}}}{2}$   II. In an  AP, if the Sum  of m  terms  is equal to the sum of n terms, then the sum of(m  + n)  terms is always  zero. Which of the  statement is given  above is/are correct?

1. A

Only I

2. B

only II

3. C

Both I  and II

4. D

None of these

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### Solution:

Statement I Since, nth term of an AP is ${\mathrm{\alpha }}_{\mathrm{n}}$  Statement II Let $a$ be the first term and d be the common difference of an AP.

According to the given condition,

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