| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2018 |
| Session | June |
| Marks | 4 |
| Topic | Geometric Sequences and Series |
| Type | Recursive sequence definition |
| Difficulty | Easy -1.2 This is a straightforward geometric progression question requiring only direct application of standard formulas. Part (i) involves simple repeated multiplication or using the nth term formula with r=0.75, and part (ii) is a direct substitution into the sum to infinity formula S=a/(1-r). Both parts are routine recall with minimal problem-solving, making this easier than average. |
| Spec | 1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1 |
**Question 1(i) and 1(ii)**
**(i)**
- $u_5 = 32 \times 0.75^4$ **M1** Attempt $u_5$ using the recurrence relationship
- $u_5 = 10.125$ **A1** Obtain 10.125; A0 for 10.1 if nothing better seen
**(ii)**
- $S_\infty = \frac{32}{1-0.75}$ **M1** Attempt to use correct sum to infinity formula, with $a = 32$ and $r = 0.75$
- $= 128$ **A1**1 A geometric progression $u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots$ is defined by $u _ { 1 } = 32$ and $u _ { n + 1 } = 0.75 u _ { n }$ for $n \geqslant 1$.\\
(i) Find $u _ { 5 }$.\\
(ii) Find $\sum _ { n = 1 } ^ { \infty } u _ { n }$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2018 Q1 [4]}}