use the backward substitution method to obtain the closed form formula for the recurrence relation

an= 2an-1 + 1, and a0 =0.

Step-by-step explanation:

So, we can infer that

and we only need to find out a formula for this sum (a geometric reason with common ratio 2)

Let's call

then,

hence,

and we have our closed formula for the sequence

3.4 pizzas

step-by-step explanation:

given is a scatter plot showing number of pizzas sold during weeks for different issues of coupon

y represents number of pizzas sold and x number of coupons issued

y is marked verticaly and x horizontally

the trend line is given as

y =3.4x+43

this says that even when no coupon is issued pizzas sold will be 43

and rate of change of pizza sold for 1 unit of coupon = slope = 3.4

i.e. when x increases by 1 unit y increases by 3.4 units

hence for each additional coupon issued 3.4 pizzas more will be sold

this is answer of 144 cubic meters