GIVEN EXPLICIT FORMULA FIND THE SPECIFIC TERMS

Given the explicit formula for an arithmetic sequence find the first five terms and the term named in the problem.

Problem 1 :

a_n = -11 + 7n, Find a₃₄

Solution:

a_n = -11 + 7n

a₅ = -11 + 7(5)

= -11 + 35

a₅ = 24

34^th term :

a₃₄ = -11 + 7(34)

= -11 + 238

a₃₄ = 227

So, first five terms are -4, 3, 10, 17, 24.

Problem 2 :

a_n = 65 - 100n

Find a₃₉

Solution:

a_n = 65 - 100n

a₅ = 65 - 100(5)

= 65 - 500

a₅ = -435

39^th term :

a₃₉ = 65 - 100(39)

= 65 - 3900

a₃₉ = -3835

So, first five terms are -35, -135, -235, -335, -435.

Problem 3 :

a_n = -7.1 - 2.1n

Find a₂₇

Solution:

a_n = -7.1 - 2.1n

a₅ = -7.1 - 2.1(5)

= -17.6

a₂₇ = -7.1 - 2.1(27)

= -7.1 - 56.7

a₂₇ = -63.8

So, first five terms are -9.2, -11.3, -13.4, -15.5, -17.6.

Problem 4 :

Solution:

Find the common difference, the explicit formula, and the term named in the problem.

Problem 5 :

31, -69, -169, -269, ...

Find a₄₀

Solution:

Explicit formula

a_n = a + (n - 1)d

Difference = -69 - 31

d = -100

a₄₀ = 31 + 39(-100)

= 31 - 3900

a₄₀ = -3869

Problem 6 :

-22, -222, -422, -622

Find a₃₂

Solution:

Explicit formula

a_n = a + (n - 1)d

Difference = -222 + 22

d = -200

a₃₂ = -22 + 31(-200)

= -22 - 6200

a₃₂ = -6222

Problem 7 :

12, 16, 20, 24,...

Find a₃₀

Solution:

Explicit formula

a_n = a + (n - 1)d

Difference = 16 - 12

d = 4

a₃₀ = 12 + 29(4)

= 12 + 116

a₃₀ = 128

Problem 8 :

0, -4, -8, -12,..

Find a₃₁

Solution:

Explicit formula

a_n = a + (n - 1)d

Difference = -4 - 0

d = -4

a₃₁ = 0 + 30(-4)

= 0 - 120

a₃₁ = -120

Problem 9 :

-10, -30, -50, -70, ...

Find a₂₁

Solution:

Explicit formula

a_n = a + (n - 1)d

Difference = -30 + 10

d = -20

a₂₁ = -10 + 20(-20)

= -10 - 400

a₂₁ = -410

Problem 10 :

11, 20, 29, 38,...

Find a₃₄

Solution:

Explicit formula

a_n = a + (n - 1)d

Difference = 20 - 11

d = 9

a₃₄ = 11 + 33(9)

= 11 + 297

a₃₄ = 308