Answer:
The function is f(n) = 10n - 13 ⇒ answer A
Step-by-step 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
