Question

Find the sum of the series 101 + 99 + 97 + .... + 47.

Answer 1

In this case, we have to first find the number of terms. 

Here a = 101, l = T_n = 47, d = 99 – 101 = –2 

∴ 47 = 101 + (n – 1) × (–2), where n = number of terms 

⇒ 47 = 101 – 2n +2 

⇒ 2n = 103 – 47 = 56 ⇒ n = 28 

∴ S_n = \(\frac{n}{2}\) (a + l) 

⇒ S₂₈ = \(\frac{28}{2}\) (101 + 47)  

= 14 × 148 

= 2072.