A geometric series has first term 18 and common ratio 1/3. What is its sum to infinity?

Worked solution for TMUA-P1-MM2-009 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1-MM2-009 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM2-009 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM2-009?

No — calculators are banned in the TMUA. TMUA-P1-MM2-009 is set for a no-calculator target of about 180 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MM2-009?

TMUA-P1-MM2-009 is Paper P1 · Sequences and series (specification code MM2), level 2. Drill more of the same topic from this page.

TMUA-P1-MM2-009 — Paper P1 · Sequences and series · Level 2

P1MM2Level 2~180s target

Spec: MM2 · No calculator · ~180s

A geometric series has first term

18

and common ratio

\frac{1}{3}

. What is its sum to infinity?

Options

$24$
$27$
$20$
$36$
it diverges

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: infinite-geometric-sum, convergence-check. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Here

|r| = \frac{1}{3} < 1

, so

S_\infty = \frac{18}{1 - 1/3} = 27

. Trap: “diverges” is plausible only if you misread

r

3

instead of

\frac{1}{3}

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Same topic · same level

P1MM2Level 2

TMUA-P1-MM2-006

A sequence is defined by u_1 = 5 and u_n+1 = 2u_n - 3. What is the value of u_3?

Sequences and series

Open TMUA-P1-MM2-006 →

Step up a 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…

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Open TMUA-P1-MM2-012 →

TMUA-P1-MM2-009 — Paper P1 · Sequences and series · Level 2

Options

Keep practising

Master Sequences and series

TMUA-P1-MM2-009 — Paper P1 · Sequences and series · Level 2

Options

Keep practising

Master Sequences and series