Question

first term of an arithmetic sequence is 3 and common difference 4.
write the algebraic form​

Answer 1

Given:

First term of an arithmetic sequence (a) = 3

Common difference (d) = 4

To find:

Write the algebraic form.

Solution:

a = 3

d = 4

tₙ = a + (n - 1)d

tₙ = 3 + (n - 1)4

tₙ = 3 + 4n - 4

tₙ = 4n - 1

where n ≥ 1

Therefore, the algebraic form is 4n - 1.

Some starting terms of the series are:

t₁ = 4×1 - 1 = 4 - 1 = 3

t₂ = 4×2 - 1 = 8 - 1 = 7

t₃ = 4×3 - 1 = 12 - 1 = 11

t₄ = 4×4 - 1 = 16 - 1 = 15

t₅ = 4×5 - 1 = 20 - 1 = 19

Answer 2

Therefore, the algebraic form is 4n - 1.