Arithmetic Progressions For Class 10 Maths Important Questions
Q 1 – Which term of A.P.: 21, 42, 63, 84………is 210?
a. 9th
b. 10th
c. 11th
d. 12th
b. 10th
Q 2 – If the common difference of an A.P is 5, then what is a18 – a13?
a. 5
b. 20
c. 25
d. 30
c. 25
Q 3 – The 17th term of an A.P. exceeds the 10th term by 14. Then the common difference is:
a. -1
b. 1
c. -2
d. 2
d. 2
Q 4 – For what value of p are 2p+1, 13, 5p -3 in A.P?
a. 4
b. -4
c. 3
d. -p
a. 4
Q 5 – Two A.P.s have the same common difference. The first term of one of these is -1 and that of other is -8. Then the difference their 4th terms is:
a.-1
b.-8
c. 7
d. -9
c. 7
Q 6 – The interior angles of a polygon are in A.P. The smallest angle is 120° and the common difference is 5°. How many sides are there in the polygon?
a. Six
b. nine
c. sixteen
d. twelve
b. nine
Q 7 – Find the sum of first 10 terms of the A.P. x – 8, x – 2 , x + 4, ……
Q 8 – Which of the following can be the nth term of an A.P.?
3n + 1 , 2n2 + 3, n3 + n. Give reasons.
Q 9 – Find the 10th term from the end of the A.P. 8, 10, 12, 14, …. , 126
Q 10 – If the seventh term of an A.P. is 1/9 and its ninth term 1/7 is , find its 63rd term
Q 11 – The value of x for which 2(x + 10) and (3x + 2) are the three consecutive terms of an AP, is
(a) 6
(b) -6
(c) 18
(d) -18
Q 12 – If the common difference of an AP is 5, then what is a18 – a13?
(a) 5
(b) 20
(c) 25
(d) 30
Q 13 – The sum of first five multiples of 3 is
(a) 45
(b) 55
(c) 65
(d) 75
Q 14 – The number of two digit numbers which are divisible by 3 is
(a) 33
(b) 31
(c) 30
(d) 29
Q 14 – The number of two digit numbers which are divisible by 3 is
(a) 33
(b) 31
(c) 30
(d) 29
Q 15 – If the nth term of an AP is 4n + 1, then the common difference is
(a) 3
(b) b
(c) 5
(d) 6
Q 16 – In an AP, if d =- 4, n = 7 and an= 4, then a is equal to
(a) 6
(b) 7
(c) 20
(d) 28
Q 17 – The 21th term of an AP whose first two terms are -3 and 4 , is
(a) 17
(b) 137
(c) 143
(d) –143
Q 18 – What is the value of x for which 2x , (x +10) and (3x + 2) are the three consecutive terms of an AP ?
Q 19 – Is -150 a term of the AP 11, 8, 5, 2, …….?
Q 20 – Find the first four terms of an AP, whose first term is -2 and common difference is -2.
Q 21 – Find the sum of first ten multiple of 5
Q 22 – Find the sum of first 16 terms of the AP 10, 6, 2, …..
Q 23 – Which term of the AP 3, 15, 27, 39, … will be 120 more than its 21st term?
Q 24 – Find the middle term of the AP 213, 205, 197, …. 37.
Q 25 – How many terms of the AP – 6 – 11/2 and 9/2…… Are needed to give their sum Zero.
Q 26 – The sum of four consecutive number in AP is 32 and the ratio of the product of the first and last term to the product of two middle terms is 7 : 15. Find the number.
Q 27 – In an AP of 50 terms, the sum of the first 10 terms is 210 and the sum of its last 15 terms is 2565. Find the AP?
Q 28 – The first term of an AP is 3, the last term is 83 and the sum of all its terms is 903. Find the number of terms and the common difference of the AP.
Q 29 – How many terms of the Arithmetic Progression 45, 39, 33, … must be taken so that their sum is 180? Explain the double answer.
Q 30 – Assertion Common difference of the AP -5, -1, 3, 7, ………. is 4.
Reason Common difference of the AP a, a+d, a 2d, ………. is given by d a2 = a1
(a) Both assertion (A) and reason (R) are true and reason
(R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason
(R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true
Q 31– Assertion Sum of first 10 terms of the arithmetic progression – 0.5 , – 1.0, –1.5………. is 3.1.
Reason Sum of n terms of an AP is given as Sn = n/2[2a +(n-1)d] where a is first term and d common difference.
(a) Both assertion (A) and reason (R) are true and reason
(R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason
(R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Q 32 – Assertion If nth term of an AP is 7 – 4 n, then its common differences is – 4
Reason Common difference of an AP is given by d an +1 – an.
(a) Both assertion (A) and reason (R) are true and reason
(R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason
(R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Q 33 – Assertion If sum of the first n terms of an AP is given by Sn = 3n2 – 4n. Then its nth term is a n = 6n – 7
Reason : nth term of an AP, whose sum to n terms is Sn, is given by an = Sn – Sn– 1
(a) Both assertion (A) and reason (R) are true and reason
(R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason
(R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Q 34 – The nth term of an AP is (7- 4n) , then what is its common difference?
Q 35 – Find the sum of first 8 multiples of 3.
