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### Question

How many odd numbers are there between -1690 and 2188?

**A**

1939.

**B**

1940.

**C**

1938.

**D**

1941.

**Soln.**

**Ans: a**

Odd numbers are in an AP. First term $a = -1689$, common difference $d = 2$, the last term $t_n$ is given as 2187. By the AP formula, $2187 = -1689 + (n - 1) × 2$ ⇒ $n = 1 + {{2187 - (-1689)}/2} = 1939$.