Question

Write the first four terms of a sequence given the recursive rule below:

f(n) = 2 × f(n − 1) + 3 for all n > 2 and f(1) = 7

A) 7, 17, 37, 77
B) 7, 9, 11, 13
C) 7, 15, 31, 63
D)not enough information​

Answer 1

The first four terms of the sequence is : A) 7, 17, 37, 77.

Explanation:

The given function f(n) = 2 x f(n − 1) + 3

Also, f(1)= 7

FOR n= 2

f(2) = 2 x f(2-1) + 3 = 2 x f(1) + 3

= (2 x 7) + 3 = 14 + 3 = 17

⇒f(2) = 17

FOR n= 3

f(3) = 2 x f(3-1) + 3 = 2 x f(2) + 3

= (2 x 17) + 3 = 34 + 3 = 37

⇒f(3) = 37

FOR n= 4

f(4) = 2 x f(4-1) + 3 = 2 x f(3) + 3

= (2 x 37) + 3 = 74 + 3 = 77

⇒f(4) =77

So, the first four terms of the sequence are 7, 17, 37, 77.

A) is the correct option.