Mathematics · Oct / Nov 2025 · Paper 21 · Question 1
YMA01
As printed in the paper
The question as text
1. An arithmetic series starts 78 + 75 + 72 + ... Find
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
1(a)[2]
+
×−=
78 17
3
27
1(b)[2]
100 2 78
(
)
×
+
99
×−
3
2
= 7050
−
(a)
M1: Attempts to find the value of
a
+
(
n
−
1)
d
with a = 78, n = 18 and d = −3. E.g.
Award for 78 17
+
×−=
3
...
Condone slips, so for example 78 written as 87…
BUT writing 78 as 18 (which is the value of n) or 3
−as 3 are not regarded as slips
Writing down 27 scores both marks
Listing is acceptable only if they write down 27 as the answer
A1: 27
(b)
M1: Attempts the correct sum formula for 100 terms. So n = 100 must be used
(twice).
Condone with
d = ±and slips on 78 …. BUT writing 78 as 18 is not regarded as a
3
slip
100 2 78
100 2
(
)
(
Award for an attempt at
×
+
×−
or
×
+
×
99
3
78
99
3
2
2
Writing down 7050
−
scores both marks
You may see the alternative formula used, usually seen with an attempt to find
u
first.
100
100 78
(
)
Look for
+
u
condoning the same slips on 78 and
u
2
100
100
+
×±
78
99
3
A1: 7050
−
but this is not isw. Withhold this mark if they write 7050
−
and follow this
with 7050
Guidance on applications of formulae for this question:
If a candidate writes out a fully correct formula including bracketing, followed by
the correct embedded values they can be awarded M1.
E.g.
n
th
term
=
a
+
(
n
−
1)
d
18
th
term
=
78
+
(18 1)
−
−
3
= 92 should be awarded M1, A0
as the correct formula and embedded values are seen
However,
18
th
term
=
78
+
(18 1)
−
−
3
= 92 should be awarded M0 as the correct
formula cannot be implied
Similarly writing
18
th
term
=
78 19
+
×−=
3
...
should be awarded M0, A0 as it implies
the incorrect formula
a
+
(
n
+
1)
d
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