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Answer

↓Steps Explained:↓

Final Answer

And the Sum of the first 15 terms for:

2,4,6,8,10

Explicit Formula

a_n = a₁ + (n - 1)d

Define d

d = Δ between consecutive terms

d = a_n - a_{n - 1}

We see a common difference = 2

We have a₁ = 2

a_n = 2 + 2(n - 1)

Calculate Term (6)

Plug in n = 6 and d = 2

a₆ = 2 + 2(6 - 1)

a₆ = 12

a₆ = 2 + 2(5)

a₆ = 2 + 10

Calculate Term (7)

Plug in n = 7 and d = 2

a₇ = 2 + 2(7 - 1)

a₇ = 14

a₇ = 2 + 2(6)

a₇ = 2 + 12

Calculate Term (8)

Plug in n = 8 and d = 2

a₈ = 2 + 2(8 - 1)

a₈ = 16

a₈ = 2 + 2(7)

a₈ = 2 + 14

Calculate Term (9)

Plug in n = 9 and d = 2

a₉ = 2 + 2(9 - 1)

a₉ = 18

a₉ = 2 + 2(8)

a₉ = 2 + 16

Calculate Term (10)

Plug in n = 10 and d = 2

a₁₀ = 2 + 2(10 - 1)

a₁₀ = 20

a₁₀ = 2 + 2(9)

a₁₀ = 2 + 18

Calculate Term (11)

Plug in n = 11 and d = 2

a₁₁ = 2 + 2(11 - 1)

a₁₁ = 22

a₁₁ = 2 + 2(10)

a₁₁ = 2 + 20

Calculate Term (12)

Plug in n = 12 and d = 2

a₁₂ = 2 + 2(12 - 1)

a₁₂ = 24

a₁₂ = 2 + 2(11)

a₁₂ = 2 + 22

Calculate Term (13)

Plug in n = 13 and d = 2

a₁₃ = 2 + 2(13 - 1)

a₁₃ = 26

a₁₃ = 2 + 2(12)

a₁₃ = 2 + 24

Calculate Term (14)

Plug in n = 14 and d = 2

a₁₄ = 2 + 2(14 - 1)

a₁₄ = 28

a₁₄ = 2 + 2(13)

a₁₄ = 2 + 26

Calculate Term (15)

Plug in n = 15 and d = 2

a₁₅ = 2 + 2(15 - 1)

a₁₅ = 30

a₁₅ = 2 + 2(14)

a₁₅ = 2 + 28

Calculate S_n:

Substituting n = 15, we get: