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Andhra Pradesh SSC (Class 10) Arithmetic Progression — practice questions

Explore 95 free Arithmetic Progression questions in Andhra Pradesh SSC (Class 10) 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 95.

Find the sum of the first $40$ positive integers divisible by $6$.Read the answer and worked solution →If the sum of the first $n$ terms of an AP is $S_n=4n-n^2$, what is the $n$th term of the AP?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 →If an AP has first term $a=6$ and common difference $d=-3$, which of the following is the correct AP?Read the answer and worked solution →The list $-1.0, -1.5, -2.0, -2.5, \ldots$ is an AP. What is its common difference?Read the answer and worked solution →Which of the following lists is an arithmetic progression?Read the answer and worked solution →In an arithmetic progression, the nth term is given by:Read the answer and worked solution →In an AP, the common difference d is found as:Read the answer and worked solution →The sum of the first n terms of an AP is:Read the answer and worked solution →If the last term is l, the sum of the first n terms of an AP is:Read the answer and worked solution →The common difference of the AP 2, 5, 8, 11, … is:Read the answer and worked solution →The 10th term of the AP 2, 7, 12, … is:Read the answer and worked solution →The common difference of the AP 3, 1, −1, −3, … is:Read the answer and worked solution →Which of the following sequences is an arithmetic progression?Read the answer and worked solution →If the first term of an AP is 5 and the common difference is 3, its 4th term is:Read the answer and worked solution →The sum of the first 10 natural numbers (1, 2, 3, …, 10) is:Read the answer and worked solution →The sum of the first n positive integers is given by:Read the answer and worked solution →If the nth term of an AP is $a_n = 3n + 2$, its common difference is:Read the answer and worked solution →How many two-digit numbers are divisible by 3 (i.e. the AP 12, 15, …, 99)?Read the answer and worked solution →The distance between two points $P(x_1,y_1)$ and $Q(x_2,y_2)$ is:Read the answer and worked solution →The distance of the point $P(x,y)$ from the origin is:Read the answer and worked solution →The midpoint of the segment joining $(x_1,y_1)$ and $(x_2,y_2)$ is:Read the answer and worked solution →The distance between the origin and the point $(3,4)$ is: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
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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 $n$ terms of an AP is $S_n=4n-n^2$, what is the $n$th term of the AP?

  1. $5-2n$
  2. $4-n$
  3. $3-2n$
  4. $5-n$
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Correct answer: A. $5-2n$

The $n$th term is $a_n=S_n-S_{n-1}$. Here, $$S_{n-1}=4(n-1)-(n-1)^2=4n-4-(n^2-2n+1)= -n^2+6n-5.$$ So $$a_n=(4n-n^2)-(-n^2+6n-5)=5-2n.$$ Hence the $n$th term is $5-2n$.

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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. $S_n=n^2+n$
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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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