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

1.	Find the sum of the series 101 + 99 + 97 + .... + 47.
Answer» 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.

Answer»

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.

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