4. Exam Challenge: Working Backwards
Problem: A GP has a first term of 40 and a Sum to Infinity of 100. Find the 2nd term.
Step 1: Build the Equation
Tap a number below, then tap the correct empty box in the formula.
$$ \frac{\text{Box A}}{1-r} = \text{Box B} $$
$=$
?
$1-r$
?
40
100
Step 2: Rearrange
We established that: $\frac{40}{1-r} = 100$.
Rearrange this to find the value of $(1-r)$.
$$ 1-r = \frac{40}{100} $$
$$ 1-r = \dots $$
Step 3: Solve for r
You found: $1 - r = 0.4$.
What is $r$?
$r =$
Step 4: Find the 2nd Term
Finally, calculate $u_2 = a \times r$.
($a=40, r=0.6$)
$u_2 =$