Why isn't the answer to TMUA-P1-MM2-012 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM2-012 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM2-012?

No — calculators are banned in the TMUA. TMUA-P1-MM2-012 is set for a no-calculator target of about 240 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MM2-012?

TMUA-P1-MM2-012 is Paper P1 · Sequences and series (specification code MM2), level 3. Drill more of the same topic from this page.

TMUA-P1-MM2-012 — Paper P1 · Sequences and series · Level 3

P1MM2Level 3~240s target

Spec: MM2 · No calculator · ~240s

An arithmetic series has first term

7

and common difference

4

. What is the smallest

n

such that the sum of the first

n

terms exceeds

500

Options

$13$
$14$
$15$
$16$
$25$

Letters only — the answer key is hidden. Work it out, then check the solution below.

Hint (check trope)

No written hint yet — check the trope: series-inequality, rounding-direction. Name the trap first, work the stem by hand, then open the solution below.

Show solution

S_n = 2n^2 + 5n

. Since

S_{14} = 462

and

S_{15} = 525

, the first

n

exceeding

500

15

. Trap:

14

comes from solving

2n^2 + 5n = 500

approximately (

n \approx 14.6

) and rounding down instead of up.

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Same topic · same level

P1MM2Level 3

TMUA-P1-MM2-013

The expansion of (1 + 4x)^6 begins 1 + 24x + cx^2 +. What is the value of c?

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Open TMUA-P1-MM2-013 →

TMUA-P1-MM2-012 — Paper P1 · Sequences and series · Level 3

Options

Keep practising

Master Sequences and series

TMUA-P1-MM2-012 — Paper P1 · Sequences and series · Level 3

Options

Keep practising

Master Sequences and series