Solve by unfolding a0 2 and for n 1 an 7a n1 3 Hint This

Solve by unfolding: a0 = 2, and for n > = 1, an = 7a n-1 +3 Hint: This one will involve applying the geometric sum formula.

Solution

ao = 2

an = 7a(n-1) + 3

an = 7(7a(n-2) + 3) + 3

an = 7(7(7a(n-3) + 3) + 3

an = 7^(n)* a0 + 3(1+7 + 7^2 +...... + 7^(n-1))

an = 7^(n) * a0 + 3 * [7^(n)-1]/ (7-1)

an = 2*7^(n) + 7^(n)/2 - 1/2

an = 5/2 * (7)^(n) - 1/2

Hence the general term for this expression is an = 5/2 * (7)^(n) - 1/2