Question

Calculate, to four decimal places, the first ten terms of the sequence. an = 1 + − 1 2 n

Answer 1

The sum of the first ten terms of the given sequence when approximated to four decimal places is; 9.6758

What is the sum of the sequence?

We are given the formula for the sequence as;

aₙ = 1 + (⁻¹/₂)ⁿ

Thus;

First term; a₁ = 1 + (⁻¹/₂)¹ = 0.5

a₂ = 1 + (⁻¹/₂)² = 1.25

a₃ = 1 + (⁻¹/₂)³ = 0.875

a₄ = 1 + (⁻¹/₂)⁴ = 1.0625

Fifth term; a₅ = 1 + (⁻¹/₂)⁵ = 0.96875

a₆ = 1 + (⁻¹/₂)⁶ = 1.01563

a₇ = 1 + (⁻¹/₂)⁷ = 0.99219

a₈ =  1 + (⁻¹/₂)⁸ = 1.00391

a₉ = 1 + (⁻¹/₂)⁹ =  0.99805

Tenth term; a₁₀ = 1 + (⁻¹/₂)¹⁰ = 1.0098

Thus, sum of all those ten terms is;

S₁₀ = 9.6758

Read more about sum of sequence at; brainly.com/question/27201995