Question

A) Find the 15th term of a linear sequence (AP) whose 5th term is 30 and 20th term is

75.
B) The second and the fourth terms of an exponential sequence (GP) of positive terms
are 9 and 4 respectively. Find
D) The common ratio;
i) The first term
2. Solve for x and y in the following equations: 2(x+4y) = 1.22+8y
​

Answer 1

A) 60

B) Common ratio, r, = 2/3

The first term, a, = 13.5

Explanation:

A)

The formula for the nth term of a linear sequence is an+b. So we can say:

30=5a+b

75=20a+b

which means

b=30-5a

b=75-20a

30-5a=75-20a

15a=45

a=3

30=5(3)+b

b=30-15=15

So our formula is 3n+15. Sub in 15 for n to find the 15th term: 3(15)+15=45+15=69

B)

The formula for the nth term of an exponential sequence is arⁿ⁻¹, where a is the first term of the sequence and r is the common ratio. Therefore we can say: 9=ar, and 4=ar³, which means a=9/r and a=4/r³

9/r=4/r³

9r³=4r

9r²=4

r=√(4/9)=2/3

9=a(2/3)

a=27/2=13.5