1). 56.862). 51.263). 48.754). 33.75

1.	1). 56.862). 51.263). 48.754). 33.75
Answer» Given, ⇒ Average = Sum of terms/Number of terms For Arithmetic Progression, If Sum of terms = S_n and first term of progression = a, COMMON DIFFERENCE = d and n = number of terms- $(\Rightarrow {S_n} = \frac{n}{2}\left( {2a + (n - 1} \right)d))$ For given SERIES - a = 10, d = 2.5 and n = 20 $(\Rightarrow {S_{20}} = \frac{{20}}{2}\left\{ {2 \times 10 + \left( {20 - 1} \right) \times 2.5} \right\})$ ⇒ S₂₀ = 10{20 + 19 × 2.5} ⇒ S₂₀ = 10(20 + 47.5) ⇒ S₂₀ = 10 × 67.5 ⇒ S₂₀ = 675 Average of first 20 terms of Arithmetic Progression = 675/20 = 33.75 ∴ Average of first 20 terms of Arithmetic Progression = 33.75

Answer»

Given,

⇒ Average = Sum of terms/Number of terms

For Arithmetic Progression,

If Sum of terms = S_n and first term of progression = a, COMMON DIFFERENCE = d and n = number of terms-

$(\Rightarrow {S_n} = \frac{n}{2}\left( {2a + (n - 1} \right)d))$

For given SERIES -

a = 10, d = 2.5 and n = 20

$(\Rightarrow {S_{20}} = \frac{{20}}{2}\left\{ {2 \times 10 + \left( {20 - 1} \right) \times 2.5} \right\})$

⇒ S₂₀ = 10{20 + 19 × 2.5}

⇒ S₂₀ = 10(20 + 47.5)

⇒ S₂₀ = 10 × 67.5

⇒ S₂₀ = 675

Average of first 20 terms of Arithmetic Progression = 675/20 = 33.75

∴ Average of first 20 terms of Arithmetic Progression = 33.75

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