Moderate -0.8 This is a straightforward application of standard arithmetic progression formulas. Given a₁=6, a₅=12, students find d=1.5 using the nth term formula, then solve S_n=90 using the sum formula to get a quadratic in n. All steps are routine with no conceptual challenges—easier than average but requires careful algebraic manipulation.
3 The first term of an arithmetic progression is 6 and the fifth term is 12 . The progression has \(n\) terms and the sum of all the terms is 90 . Find the value of \(n\).
$1^{\text{st}} \text{ term} = a = 6$ | B1 | Correct value of $d$
$5^{\text{th}} \text{ term} = a + 4d = 12 \rightarrow d = 1.5$ | M1 | Use of correct formula with his $d$
$S_n = \frac{n}{2}(12 + (n-1)1.5) = 90$ | DM1, A1 | Correct method for soln of quadratic. Co (ignore inclusion of $n = -15$)
$\rightarrow n^2 + 7n - 120 = 0 \rightarrow n = 8$
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3 The first term of an arithmetic progression is 6 and the fifth term is 12 . The progression has $n$ terms and the sum of all the terms is 90 . Find the value of $n$.
\hfill \mbox{\textit{CAIE P1 2008 Q3 [4]}}