For each integer $n>1$ , if $S(n)$ denotes the sum of even integers up to $n$ (not inclusive of $n$ ). For example, $S(10)=2+4+6+8=20$ . What is the value of $S(300)$ ?

Answer Choices

Correct answer marked below

22050

22350

Correct

22650

45150

90300

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Comments

SebastianJun 19

Took me a while to realize S(300) sums even numbers up to 300, not including 300. So it's 2 + 4 + ... + 298. Then factor out 2 and sum 1 to 149. Sum formula n(n+1)/2 gives 149*150/2 = 11175, times 2 = 22350. Nice question, but the wording almost got me.

KonstantinaJul 3

Exactly! I initially included 300 and got a different number, then saw none of the answers matched. Sneaky but fair.

RheaJun 27

Same here. The example S(10)=20 made it clear though.

YaminaJul 4

Is there a quick way to do this without summing 1 to 149? Like a formula for sum of evens?

LienJul 7

Sum of first k even numbers is k(k+1). Here k = 149, so 149*150 = 22350.

ArvindSep 22

This felt like a solid medium. The trick is just recognizing you can factor out 2 and then it's an arithmetic series. I almost started adding manually like a dummy.

What this question tests

What it tests

Your ability to spot and extend arithmetic and geometric sequences and work with recursive definitions.

Common trap

Off-by-one errors in indexing (a₀ vs a₁) or confusing an arithmetic difference with a geometric ratio.

For each integer n>1n>1n>1, if S(n)S(n)S(n) denotes the sum of even integers up to nnn (not inclusive of nnn). For example, S(10)=2+4+6+8=20S(10)=2+4+6+8=20S(10)=2+4+6+8=20. What is the value of S(300)S(300)S(300)?