Moderate -0.8 This is a straightforward sum to infinity question with clear geometric progression setup (r=0.98). Students only need to identify the GP parameters and apply the standard formula S∞=a/(1-r), requiring minimal problem-solving beyond recognizing the context.
3 A particular phone battery will last 10 hours when it is first used. Every time it is recharged, it will only last \(98 \%\) of its previous time.
Find the maximum total length of use for the battery.
Use of GP with common ratio 0.98. GP implied by formula for \(S_\infty\), \(S_n\) or \(u_n\) showing 0.98 or 1st 3 terms
\(\frac{10}{1-0.98}\)
M1
Sum to infinity
\(500\)
A1
## Question 3:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $10 + 10\times0.98 + 10\times0.98^2$ or $10 + 9.8 + 9.604$ | M1 | Use of GP with common ratio 0.98. GP implied by formula for $S_\infty$, $S_n$ or $u_n$ showing 0.98 or 1st 3 terms |
| $\frac{10}{1-0.98}$ | M1 | Sum to infinity |
| $500$ | A1 | |
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3 A particular phone battery will last 10 hours when it is first used. Every time it is recharged, it will only last $98 \%$ of its previous time.
Find the maximum total length of use for the battery.
\hfill \mbox{\textit{OCR MEI Paper 3 2020 Q3 [3]}}