Moderate -0.8 This is a straightforward geometric progression question requiring only basic recall of GP formulas. Students need to use b² = 32 × 12.5 to find b = 20, then r = 0.625, and apply the standard sum formula S₁₅ = a(1-r¹⁵)/(1-r). It's simpler than average as it involves direct application of well-practiced formulas with no conceptual challenges or problem-solving required.
A geometric progression has a positive common ratio. Its first three terms are 32, \(b\) and 12.5.
Find the value of \(b\) and find also the sum of the first 15 terms of the progression. [5]
Question 2:
2 | b 12.5
oe
32 b
b = 20
r = 0.625 soi
10.62515
32
oe or ft their r
10.625
85.259... to 3 s.f. or more | M1
A1
A1
M1
A1
[5] | or r2 = 12.5/32
M0 if directly summed, but B2 if correct
answer obtained to 3 s.f. or better | B3 for both r and b www; B2 for one
of these
A geometric progression has a positive common ratio. Its first three terms are 32, $b$ and 12.5.
Find the value of $b$ and find also the sum of the first 15 terms of the progression. [5]
\hfill \mbox{\textit{OCR MEI C2 Q2 [5]}}