Moderate -0.8 This is a straightforward application of arithmetic progression formulas requiring students to set up two simultaneous equations from given terms, solve for a and d, then apply the sum formula. The calculations are routine with no conceptual challenges beyond basic AP knowledge, making it easier than average but not trivial due to the multi-step nature.
An arithmetic progression has tenth term 11.1 and fiftieth term 7.1. Find the first term and the common difference. Find also the sum of the first fifty terms of the progression. [5]
Question 1:
1 | a + (10 – 1)d = 11.1 and a + (50 − 1)d = 7.1
d = −0.1
a = 12
1
×50(theira+7.1) with a > 11.1
2
955
477.5 or 477½ or cao
2 | M1
A1
A1
M1
A1
[5] | may be implied by 40d = ±4 or embedded
in attempt to solve
if unsupported, B2 for one of these and B3
for both
50
or (2a+(50−1)d)with a > 11.1 and
2
d < 0 | condone one slip in coefficient of d
if M0, B2 for any form of correct
answer www
An arithmetic progression has tenth term 11.1 and fiftieth term 7.1. Find the first term and the common difference. Find also the sum of the first fifty terms of the progression. [5]
\hfill \mbox{\textit{OCR MEI C2 Q1 [5]}}