Question

In a certain sequence of numbers, each term after the first is found by doubling and then adding $3$ to the previous term. If the seventh term of the sequence is $125$, what is the first term?

Answer 1

We know that
an=[a(n-1)]*2+3
if a7=125 
a) Find a1

step 1
find a6
a7=a6*2+3--------> a6=(a7-3)/2-----> a6=(125-3)/2----> a6=61

step 2
find a5
a6=a5*2+3--------> a5=(a6-3)/2-----> a5=(61-3)/2----> a5=29

step 3
find a4
a5=a4*2+3--------> a4=(a5-3)/2-----> a4=(29-3)/2----> a4=13

step 4
find a3
a4=a3*2+3--------> a3=(a4-3)/2-----> a3=(13-3)/2----> a3=5

step 5
find a2
a3=a2*2+3--------> a2=(a3-3)/2-----> a2=(5-3)/2----> a2=1

step 6
find a1
a2=a1*2+3--------> a1=(a2-3)/2-----> a1=(1-3)/2----> a1=-1

the answer is
a1=-1