Moderate -0.3 This is a straightforward geometric sequence problem requiring standard techniques: finding the common ratio from two given terms (solving r³ = -8), then calculating the tenth term and deriving the sum formula. While it involves multiple steps and negative ratio handling, it's a routine textbook exercise with no novel problem-solving required, making it slightly easier than average.
5 The second term of a geometric sequence is 6 and the fifth term is - 48 .
Find the tenth term of the sequence.
Find also, in simplified form, an expression for the sum of the first \(n\) terms of this sequence.
allow M1 for \(a=6\div\) their \(r\) and substitution in GP formula with their \(a\) and \(r\)
\((-2)^n - 1\)
A1
c.a.o.
**Question 5:**
| Answer | Mark | Guidance |
|--------|------|----------|
| $ar = 6$ and $ar^4 = -48$ | **M1** | **B2** for $r=-2$ www | ignore incorrect lettering such as $d=-2$ |
| $r = -2$ | **M1** | | |
| tenth term $= 1536$ | **A1** | **B3** for 1536 www | |
| $\frac{-3(1-(-2)^n)}{1-(-2)}$ o.e. | **M1** | allow **M1** for $a=6\div$ their $r$ and substitution in GP formula with their $a$ and $r$ | condone the omission of the brackets round "$-2$" in the numerator and/or the denominator |
| $(-2)^n - 1$ | **A1** | c.a.o. | |
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5 The second term of a geometric sequence is 6 and the fifth term is - 48 .\\
Find the tenth term of the sequence.\\
Find also, in simplified form, an expression for the sum of the first $n$ terms of this sequence.
\hfill \mbox{\textit{OCR MEI C2 2011 Q5 [5]}}