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

Worked solution for TMUA-P1-MM2-013 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1-MM2-013 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM2-013 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM2-013?

No — calculators are banned in the TMUA. TMUA-P1-MM2-013 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-MM2-013?

TMUA-P1-MM2-013 is Paper P1 · Sequences and series (specification code MM2), level 3. Drill more of the same topic from this page.

TMUA-P1-MM2-013 — Paper P1 · Sequences and series · Level 3

P1MM2Level 3~240s target

Spec: MM2 · No calculator · ~240s

The expansion of

(1 + 4x)^6

begins

1 + 24x + cx^2 + \dots

. What is the value of

c

Options

$60$
$240$
$360$
$480$
$24$

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: binomial-expansion, inner-power-trap. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Expand:

(1+4x)^6 = 1 + 6(4x) + 15(4x)^2 + \dots = 1 + 24x + 240x^2 + \dots

. Trap:

60

15 \times 4

— plausible if you multiply by

4

once instead of

4^2

Keep practising

Same topic · same level
P1MM2Level 3
TMUA-P1-MM2-012
An arithmetic series has first term 7 and common difference 4. What is the smallest n such that the sum of the first n t…
Sequences and series
Open TMUA-P1-MM2-012 →
Same trap: inner-power-trap
P1MM2Level 2
TMUA-P1-MM2-010
What is the coefficient of x^2 in the expansion of (1 + 3x)^5?
Sequences and series
Open TMUA-P1-MM2-010 →
More in this topic
P1MM2Level 3
TMUA-P1-MM2-019
Find 16 + 8 + 4 + ·s (sum to infinity).
Sequences and series
Open TMUA-P1-MM2-019 →

Browse more

Loading…

Keep practising

Same topic · same level

P1MM2Level 3

TMUA-P1-MM2-012

An arithmetic series has first term 7 and common difference 4. What is the smallest n such that the sum of the first n t…

Sequences and series

Open TMUA-P1-MM2-012 →

Same trap: inner-power-trap

P1MM2Level 2

TMUA-P1-MM2-010

What is the coefficient of x^2 in the expansion of (1 + 3x)^5?

Sequences and series

Open TMUA-P1-MM2-010 →

TMUA-P1-MM2-013 — Paper P1 · Sequences and series · Level 3

Options

Keep practising

Master Sequences and series

TMUA-P1-MM2-013 — Paper P1 · Sequences and series · Level 3

Options

Keep practising

Master Sequences and series