The first two terms in a geometric series are 20, 22. to two decimal places, the sum of the first k terms of the series is 271.59. find k.

k=9

Step-by-step explanation:

First find r=22/20=1.1

The sum of the first k terms formula is a1•(1-r^k)/(1-r)

a1=20 and the sum is 271.59

Now plug in these values in the formula and find k.

271.59=20(1-1.1^k)/(1-1.1)

When you simplify this equation, you will get k=ln(2.358)/ln(1.1)

k=9

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt