Question

Consider the sequence -3,7,17,27...

which function (with domain all integers n>=1) could be used to define and continue the sequence.

A f(n)= 10n-13
B f(n)=-3n+10
C f(n)=10n-3
D f(n)=-3(n-1)+10

Answer 1

The function is f(n) = 10n - 13 ⇒ answer A

Explanation:

* Lets revise the arithmetic sequence

- There is a constant difference between each two consecutive

numbers

- Ex:

# 2 , 5 , 8 , 11 , ……………………….

# 5 , 10 , 15 , 20 , …………………………

# 12 , 10 , 8 , 6 , ……………………………

* General term (nth term) of an Arithmetic sequence:

# U1 = a , U2 = a + d , U3 = a + 2d , U4 = a + 3d , U5 = a + 4d

# Un = a + (n – 1)d, where a is the first term , d is the difference

between each two consecutive terms, n is the position of the

term in the sequence

* Now lets solve the problem

- The sequence is -3 , 7 , 17 , 27 , .........

∵ 7 - (-3) = 7 + 3 = 10

∵ 17 - 7 = 10

∵ 27 - 17 = 10

∴ The sequence is arithmetic with constant difference 10

∴ f(n) = a + (n - 1)d

∵ a = -3

∵ d = 10

∴ f(n) = -3 + (n - 1)(10) ⇒ lets simplify it

∴ f(n) = -3 + n(10) + (-1)(10) = -3 + 10n - 10 ⇒ add like terms

∴ f(n) = 10n - 13

* The function is f(n) = 10n - 13