MULTIPLE CHOICE QUESTIONS ( MCQ’s )
1. In an AP, if d = – 4, n = 7, an = 4, then a is ____
(a) 6
(b) 7
(c) 20
(d) 28
2. In an AP, if a = 3.5, d = 0, n = 101, then an will be _____
(a) 0
(b) 3.5
(c) 103.5
(d) 104.5
3. The first four terms of an AP, whose first term is –2 and the
common difference is –2, are______
(a) –2, 0, 2, 4
(b) –2, 4, –8, 16
(c) –2, –4, –6, – 8
(d) –2, –4, –8, –16
4. In an AP if a = 1, an = 20 and Sn = 399, then n is_____
(a) 19
(b) 21
(c ) 38
(d ) 42
5. If the common difference of an AP is 5, then what is a18 – a13.
(a) 5
(b) 20
(c) 25
(d) 30
6. The sum of first 16 terms of the AP: 10, 6, 2,… is _____
(a) –320
(b) 320
(c) –352
(d) –400
7. The middle most term(s) of the AP: –11, –7, –3, …, 49 is _____
(a) 18, 20
(b) 19, 23
(c) 17.
(d ) 23, 25
8. The 21st term of the AP whose first two terms are –3 and 4 is _____
(a) 17
(b) 137
(c) 143
(d) –143
9. If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th term?
(a) 30
(b) 33
(c) 37
(d) 38
10. Two AP’s have the same common difference. The first term of one of these is – 1 and that of the other is – 8. Then the difference between their 4th terms is___
(a) –1
(b) – 8
(c) 7
(d) – 9
11. Consider the list of numbers −4 , −3, −2, −1, 0 ……. each of the numbers
in the list is called a ______ .
(a) Clue
(b) Progression
(c) Form
(d) Term
12. The general form of an A.P is _____
(a) a, a + 4d
(b) a, a + 3d ,
(c) a, a + 5d
(d) none of the above
13. For the A.P 3/4 , 1/4 , −1/4, −3/4……….
the first term ‘a’ and common difference ‘d’ will be _____
(a) 3/4, +1
(b) 3/4 , −1
(c) 3/4 , 0
(d) −3/4 , −1
14. The nth term of the AP with first term ‘a’ and common difference ‘d’ is given by_____
(a){ a }_{ n } = a+(n-1) d
(b) { a }_{ n } = a+(n+1) d
(c) { a }_{ n } = 2a+(n-1) d
(d) { a }_{ n } = 2a+(n+1) d
15. The simple interest formula is \frac { p\times t\times r }{ 100 } t = _____
(a) t=\frac { 100\times p }{ IR }
(b) t=\frac { 100\times p }{ P }
(c) t=\frac { 100\times p }{ PI }
(d) t=\frac { 100\times p }{ PR }
16 . Sn = n/2 + (a + l) . here l = ___
(a) l = a + (n−1) d
(b) l = a − (n+1) d
(c) l = a − (n−1) d
(d) l = a + (n+1) d
17 . Sum of the first ‘n’ positive integers is given Sn = ___
(a) Sn = n (n + 1)
(b) Sn = n (n + 1) 2d
(c) Sn = n (n + 1) d
(d) Sn = n (n + 1)/2
18. If a, b, c are in AP then we get b = (a + c)/2 and b is called ____
(a) Finite mean
(b) Arithmetic mean
(c) Geometric mean
(d) Algebraic mean
19. The first term of AP is 6 and its common difference is −2. Find the 18th term
(a) −28
(b)+28
(c) − 27
(d) +27
20. The ‘n’ term of an AP is (2x − 3) the common difference will be____
(a) 3
(b) 2
(c) −2
(d) −3
21. If the sum of n terms of an A.P. be 3n² + n and its common difference is 6,
then its first term is ____
(a) 2
(b) 3
(c) 1
(d) 4
22. The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36,
then the number of terms will be_____
(a) 5
(b) 6
(c) 7
(d) 8
23. The nth term of an A.P., the sum of whose n terms is Sn, is _____
(a) Sn + Sn − 1
(b) Sn − Sn − 1
(c) Sn + Sn + 1
(d) Sn − Sn +1
24. The sum of the first n odd natural numbers is ____
(a) 2n−1
(b) 2n+1
(c) n²
(d) n²−1
25. If 18, a, b, −3 are in A.P.,then a + b = ____
(a) 19
(b) 7
(c) 11
(d) 15
26.If the nth term of an A.P.is 2n + 1, then the sum of first n terms of the A.P. is____
(a) n (n−2)
(b) n (n+2)
(c) n (n+1)
(d) n (n−1)
27. The sum of the first 15 multiples of 8 is _____
(a) 920
(b) 860
(c) 900
(d) 960
28. Next term of the AP √2, 3√2, 5√2, ……. is _______
(a) 2√7
(6) 6√2
(c) 9√2
(d) 7√2
29. First four terms of the sequence an = 2n + 3 are __________
(a) 3, 5, 7, 9
(b) 5, 7, 9, 11
(c) 5, 8, 11, 14
(d) 5, 7, 8, 12
30. The 20th term of the AP −5, −3, −1, 1, is ___________–
(a) 33
(b) 30
(c) 20
(d) 25
31. The common difference of the AP … −4, −2, 0, 2, …. is ___________
(a) 2
(b) −2
(c) 12
(d) –12
32. If p – 1, p + 3, 3p – 1 are in AP, then d is equal to _____
(a) 4
(b) −4
(c) 2
(d) −2
33.The common difference of the AP … −4, −2, 0, 2, …. is ___________
(a) 2
(b) −2
(c) 12
(d) –12
34. The sum of first ten natural number is _______
(a) 55
(b) 155
(c) 65
(d) 110
35. Find the 15th term of an AP −2, −5, −8, ….
(a) 70
(b) −44
(c) 72
(d) 64
Answers. + Clues:
1. (d) ⇒ Put { a }_{ n } = a + (n−1) d
2. (b) ⇒ Put { a }_{ n } = a + (n−1) d
3. (c) ⇒ Put { a }_{ 1 }, { a }_{ 2 },{ a }_{ 3 },{ a }_{ 4 }..........({ a }_{ n }= a+(n−1) d)
4. (c) ⇒ Put { s }_{ n } = \frac { n }{ 2 } (2a + (n−1) d)
5. (c) ⇒ find{ a }_{ 18 } and { a }_{ 13 }by\quad { a }_{ n }= (a−1) d. and\quad then\quad subtract
6. (a) ⇒ Use { s }_{ n }=\frac { n }{ 2 } (2a + (n−1) d)
7. ( c) ⇒ Use { a }_{ n } = (a + (n−1) d)
8. ( b) ⇒ Find { a }_{ 21 } if { a }_{ 1 } and { a }_{ 2} are given
9. ( b)⇒ { a }_{ 2 }=13 { a }_{ 5 }=25 find { a }_{ 7 } use ({ a }_{ n } = a + (n−1) d)
10. (c) ⇒ First term { a }_{ 1 }=−1 common difference = d
{ a }_{ 2 }=−8 common difference = d
then find 4th term of each A.P.
11. (d) ⇒ Text book (5.2)
12. (d) ⇒ Definition of general form of an AP
13. (b) ⇒ Textbook example
14. (a) ⇒ Formula of AP
15. (d) ⇒ Cross multiply & get ‘T’
16. (a) ⇒ Formula in text book
17. (d) ⇒ Formula in textbook
18. (b) ⇒ Textbook summary
19. (c) ⇒ Use an = a + (n−1) d
20 .(b) ⇒ an = 2x − 3…..(1) and a1 =−1 and an = a1 − d +nd ……..(2) .Compare equations (1) and(2)
21. (d) ⇒ Use sum formula and find the first term as common difference is given
22. (b) ⇒ First and last terms are given .sum of terms is also given .Then find n
23. (b) ⇒ Textbook (Remark)
24. (c) ⇒ Use sum formula
25. (d) ⇒ Find value of a and b ( second and third term) then add them
26. (d) ⇒ Example 14 (ii) Textbook
27. (d) ⇒ Write the first few multiples of 8. Then use the sum formula
28. (d) ⇒ We have to find 4th term so use (a + 3d)
29. (b) ⇒ Put n = 1,2,3,4 and get the values.
30. (a) ⇒ We have to find 20th term so use (a + 19 d)
31. (a) ⇒ Use common difference formula
32. (a) ⇒ In the A.P a, a+d, a+2d,…..Here a = p−1 and a + d = p + 3
33. (a) ⇒ Use common difference formula
34. (a) ⇒ Use sum formula and n = 10
35. (b) ⇒ We have to find 15th term so use (a + 14 d)