Find the indicated term of the geometric sequence 5th term o

Find the indicated term of the geometric sequence. 5th term of 1, 2, 4, ... Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. 6th term is -10; 15th term is -46

Solution

Solution:

45)

Given n = 5 a₁ = 1, r = 2

a_n = a₁ * r^n-1

a_n = 1 * 2^5-1

= 16

The Fifth term is 16.

46)

Given a₆ = - 10 and a₁₅ = -46

Substitute - 10 for a₆ and - 46 for a₁₅ in the formula

an=a₁+(n1)d to obtain a system of linear equations in terms of a₁ and d

a₆=a₁+(61)d - 10 =a₁+ 5d

a₁₅ =a₁+(151)d - 46=a₁+14d

Subtract the second equation from the first equation and solve for d

36 = 9d

4 = d

d = - 4

Then - 10 =a₁+ 5 (4)). Solve for a

- 10 = a₁21

a₁ = 11

Therefore the first term is a₁ = 11

And the common difference is - 4