FIND THE RECURSIVE FORMULA FOR ARITHMETIC SEQUENCE

Given the first and the common difference of an arithmetic sequence find the recursive formula and the three terms in the sequence after the last one given.

Problem 1 :

Solution:

Recursive formula

a_n = a_n-1 + d

Problem 2 :

a₁ = 39, d = -5

Solution:

Recursive formula

a_n = a_n-1 + d

So, an arithmetic sequences are 39, 34, 29 and 24.

Problem 3 :

a₁ = -26, d = 200

Solution:

Recursive formula

a_n = a_n-1 + d

So, an arithmetic sequences are -26, 174, 374 and 574.

Problem 4 :

a₁ = -9.2, d = 0.9

Solution:

Recursive formula

a_n = a_n-1 + d

a₂ = a_2-1 + 0.9

So, an arithmetic sequences are -9.2, -8.3, -7.4 and -6.5.

Given a term in an arithmetic sequence and the common difference find the recursive formula and the three terms in the sequence after the last one given.

Problem 5 :

a₂₁ = -1.4, d = 0.6

Solution:

Recursive formula

a_n = a + (n - 1)d

a₂₁ = a + 20d

-1.4 = a + 20(0.6)

-1.4 = a + 12

a₁ = -13.4

So, first three terms are -13.4, -12.8 and -12.2.

Problem 6 :

a₂₂ = -44, d = -2

Solution:

Recursive formula

a_n = a + (n - 1)d

a22 = a + 21d

-44 = a + 21(-2)

-44 = a - 42

a₁ = -2

So, first three terms are -2, -4 and -6.

Problem 7 :

a₁₈ = 27.4, d = 1.1

Solution:

Recursive formula

a_n = a + (n - 1)d

a₁₈ = a + 17d

27.4 = a + 17(1.1)

27.4 = a + 18.7

a₁ = 8.7

So, first three terms are 8.7, 9.8 and 10.9.

Problem 8 :

a₁₂ = 28.6, d = 1.8

Solution:

Recursive formula

a_n = a + (n - 1)d

a12 = a + 11d

28.6 = a + 11(1.8)

28.6 = a + 19.8

a₁ = 8.8

So, first three terms are 8.8, 9.9 and 11.