Moderate -0.5 This is a straightforward application of arithmetic progression formulas requiring students to find the common difference from given terms, then determine the number of terms, and finally calculate the sum. While it involves multiple steps, each step uses standard AP formulas with no conceptual difficulty or problem-solving insight required, making it slightly easier than average.
4 In an arithmetic progression, the 1 st term is - 10 , the 15th term is 11 and the last term is 41 . Find the sum of all the terms in the progression.
Using \(a = (n-1)d\). Correct method – not for \(a + nd\). Co
\(a + (n-1)d = 41\); \(n = 35\)
M1, A1 [2]
Correct method – not for \(a + nd\). Co
Either \(S_n = n/2(2a + (n-1)d)\) or \(n/2(a + l) = 542.5\)
M1, M1, A1 [5]
Either of these used correctly. For his d and any n
$a = -10$; $a + 14d = 11$; $d = \frac{3}{2}$ | M1, M1, A1 [3] | Using $a = (n-1)d$. Correct method – not for $a + nd$. Co
$a + (n-1)d = 41$; $n = 35$ | M1, A1 [2] | Correct method – not for $a + nd$. Co
Either $S_n = n/2(2a + (n-1)d)$ or $n/2(a + l) = 542.5$ | M1, M1, A1 [5] | Either of these used correctly. For his d and any n
4 In an arithmetic progression, the 1 st term is - 10 , the 15th term is 11 and the last term is 41 . Find the sum of all the terms in the progression.
\hfill \mbox{\textit{CAIE P1 2003 Q4 [5]}}