Question

F(1)=7, F(n)= -4* f(n-1)+15 Find the first four terms

Answer 1

First four terms are 7, -13, 67, -253

Solution:

Given that,

$f(1) = 7$

The formula to find nth term is given as:

$f(n) = -4 \times f(n-1) + 15$

We can find the first four terms by substituting n = 2, 3, 4

First term:

f(1) = 7

Second term:

Substitute n = 2

$f(2) = -4 \times f(2-1) + 15\\\\f(2) = -4 \times f(1) + 15\\\\Substitute\ f(1) = 7\\\\f(2) = -4 \times 7 + 15\\\\Simplify\\\\f(2) = -28 + 15\\\\f(2) = -13$

Third term:

Substitute n = 3

$f(3) = -4 \times f(3-1) + 15\\\\f(3) = -4 \times f(2) + 15\\\\Substitute\ f(2) = -13\\\\f(3) = -4 \times -13 + 15\\\\Simplify\\\\f(3) = 52+15\\\\f(3) = 67$

Fourth term:

Substitute n = 4

$f(4) = -4 \times f(4-1) + 15\\\\f(4) = -4 \times f(3) + 15\\\\Substitute\ f(3) = 67\\\\f(4) = -4 \times 67 + 15\\\\Simplify\\\\f(4) = -268+15\\\\f(4) = -253$

Thus first four terms are 7, -13, 67, -253