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GRE Arithmetic Progression — practice questions

Explore 117 free Arithmetic Progression questions in GRE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Arithmetic Progression questions and exercises with answers

Showing questions 1–30 of 117.

Find the sum of the first $40$ positive integers divisible by $6$.Read the answer and worked solution →If the sum of the first $7$ terms of an AP is $49$ and that of the first $17$ terms is $289$, what is the sum of the first $n$ terms?Read the answer and worked solution →Find the sum of the first $51$ terms of an AP whose second and third terms are $14$ and $18$ respectively.Read the answer and worked solution →Find the sum of first $22$ terms of an AP in which $d=7$ and the $22$nd term is $149$.Read the answer and worked solution →The first term of an AP is $5$, the last term is $45$ and the sum is $400$. Find the number of terms and the common difference.Read the answer and worked solution →How many terms of the AP $9, 17, 25, \ldots$ must be taken to give a sum of $636$?Read the answer and worked solution →How many terms of the AP $24, 21, 18, \ldots$ must be taken so that their sum is 78?Read the answer and worked solution →Which term of the AP $21, 18, 15, \ldots$ is $-81$?Read the answer and worked solution →Reena's monthly salary forms an AP: ₹8000, ₹8500, ₹9000, $\ldots$. What will be her monthly salary in the 15th year?Read the answer and worked solution →Which of the following lists is an arithmetic progression?Read the answer and worked solution →A fair six-sided die is rolled once. What is the probability of getting an even number?Read the answer and worked solution →A **random variable** is best defined as:Read the answer and worked solution →A **discrete** random variable is one whose possible values:Read the answer and worked solution →For a continuous random variable $X$, the probability that $X$ equals any specific value is:Read the answer and worked solution →The **cumulative distribution function (c.d.f.)** $F(x)$ of a discrete random variable is:Read the answer and worked solution →When two fair dice are rolled and $X$ denotes the sum of the upper faces, the range of $X$ is:Read the answer and worked solution →If a fair coin is tossed twice and $X$ = number of heads, then $P[X = 1]$ equals:Read the answer and worked solution →If two cards are drawn with replacement from a deck of 52, $P[X = 2]$ where $X$ = number of aces equals:Read the answer and worked solution →A fair die is thrown. Let $X$ = number of factors of the number on the upper face. $P[X = 2]$ equals:Read the answer and worked solution →$f(x) = 3x^2$ for $0 < x < 1$ is the p.d.f. of $X$. The probability $P[1/2 < X < 1]$ is:Read the answer and worked solution →If $f(x) = kx^2(1 - x)$ for $0 < x < 1$ is the p.d.f. of $X$, the value of $k$ is:Read the answer and worked solution →For p.d.f. $f(x) = x/8$, $0 < x < 4$, the probability $P[x < 1.5]$ is:Read the answer and worked solution →Find $k$ if $f(x) = kx$ for $0 < x < 2$ and 0 otherwise is a valid p.d.f.Read the answer and worked solution →The c.d.f. $F(x)$ of the p.d.f. $f(x) = 3x^2$ for $0 < x < 1$ is:Read the answer and worked solution →Two cards are drawn with replacement. $X$ = number of aces. The probability $P[X \geq 1]$ equals:Read the answer and worked solution →For p.d.f. $f(x) = x^2/3$ for $-1 < x < 2$, the probability $P[0 < X \leq 1]$ equals:Read the answer and worked solution →For p.d.f. $f(x) = k(4 - x^2)$ for $-2 \leq x \leq 2$ (and 0 elsewhere), the value of $k$ is:Read the answer and worked solution →For the c.d.f. $F(x) = 3x - 2x^3$ (from p.d.f. $f(x) = 3(1 - 2x^2)$ on $[0, 1]$), $F(0.5)$ equals:Read the answer and worked solution →If a fair coin is tossed $n$ times, the probability of any exact pattern (like all heads) is:Read the answer and worked solution →If a die is thrown and 'getting an odd number' is success, then $p$ and $q$ are:Read the answer and worked solution →

Worked practice questions

Find the sum of the first $40$ positive integers divisible by $6$.

  1. 4680
  2. 4920
  3. 5100
  4. 5280
Show answer and solution

Correct answer: B. 4920

The first 40 positive integers divisible by 6 are $6,12,18,\ldots,240$, an AP with $a=6$, $d=6$, and $n=40$. So $$S_{40}=\frac{40}{2}(6+240)=20\cdot 246=4920.$$

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If the sum of the first $7$ terms of an AP is $49$ and that of the first $17$ terms is $289$, what is the sum of the first $n$ terms?

  1. $S_n=n^2$
  2. $S_n=n(2n-1)$
  3. $S_n=n(n+1)$
  4. $S_n=n^2+n$
Show answer and solution

Correct answer: A. $S_n=n^2$

For an AP, $S_n=\frac{n}{2}[2a+(n-1)d]$. Given $$\frac{7}{2}(2a+6d)=49 \Rightarrow a+3d=7$$ and $$\frac{17}{2}(2a+16d)=289 \Rightarrow a+8d=17.$$ Subtracting gives $5d=10$, so $d=2$. Then $a+6=7$, hence $a=1$. Therefore $$S_n=\frac{n}{2}[2+(n-1)2]=\frac{n}{2}(2n)=n^2.$$

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Find the sum of the first $51$ terms of an AP whose second and third terms are $14$ and $18$ respectively.

  1. 5202
  2. 5253
  3. 5304
  4. 5355
Show answer and solution

Correct answer: B. 5253

Let the first term be $a$ and common difference be $d$. Then $$a+d=14, \quad a+2d=18.$$ Subtracting gives $d=4$, so $a=10$. Now $$S_{51}=\frac{51}{2}[2\cdot 10+(51-1)\cdot 4]=\frac{51}{2}(20+200)=\frac{51}{2}\cdot 220=51\cdot 110=5610.$$ Therefore the sum is $5610$.

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More Mathematics topics

MathematicsStatistics and ProbabilitySets and RelationsQuadratic EquationsReal Numbers and PolynomialsUnit 1A1: Relations, Functions and GraphsUnit 6B: Definite Integration & Riemann SumsUnit 1B1: Limit Concepts and Graphical Limits