### Question

**How do I solve 1 + 3 + 5 + 7 +… + 101?**

A. 2421

B. 2601

C. 2341

D. 2701

#### Answer: B. 2601

**Solution:**

**This series is an arithmetic progression**

**1, 3, 5, 7, ………, 101**

Having First No (a) = 1, Last No (tn) = 101 and

Common difference (d) = Previous no – Next No = 3 – 1 = 5 – 3 = 7 – 5 = 2

According to formula

tn = [a + (n-1) d] where n is no of terms

=> 101 = 1 + (n – 1) * 2

=> 101 – 1 = (n – 1) * 2

=> 100 / 2 = n – 1

=> 50 + 1 = n

**=> n = 51**

**According to sum formula**

Sn = [n * (a + l) ] / 2

= [51 * (1 + 101) ] / 2

= (51 * 102) / 2

= 51 * 51

**Sn = 2601**

Hence, The answer is **2601.**

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