| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2022 |
| Session | June |
| Marks | 5 |
| Topic | Geometric Sequences and Series |
| Type | Find sum to infinity |
| Difficulty | Standard +0.3 This is a straightforward geometric series problem requiring finding the common ratio from two terms, then calculating an infinite sum starting from n=5. The steps are routine: use u₄/u₂ = r² to find r = 1/√2, find the first term, then apply the standard infinite GP sum formula with appropriate adjustment for starting at n=5. Slightly easier than average as it follows a standard template with no conceptual surprises. |
| Spec | 1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1 |
A geometric series has second term 16 and fourth term 8
All the terms of the series are positive.
The $n$th term of the series is $u_n$
Find the exact value of $\sum_{n=5}^{\infty} u_n$ [5 marks]
\hfill \mbox{\textit{SPS SPS SM Pure 2022 Q9 [5]}}