Mathematics Multiple Choice Questions & Answers on “Nth Term of Arithmetic Progression”.
1. What will be the nth term of the AP 1, 5, 9, 13, 17…….?
a) 4n – 3
b) 3n – 4
c) 4n + 3
d) 3n + 4
Answer: a
Clarification: Here a = 1 and d = 4
The nth term of the AP = a + (n – 1)d = 1 + (n – 1)4 = 1 + 4n – 4 = 4n – 3
2. If the nth term of the AP is 2n + 7, then the common difference will be _____
a) -2
b) 2
c) 3
d) -3
Answer: b
Clarification: nth term of the AP is 2n + 7
Tn = 2n + 7
Common difference = T2 – T1 = (2 × 2 + 7 – (2 × 1 + 7)) = 11 – 9 = 2
3. If the nth term of the AP is 7n – 9, then the first term is ________
a) 1
b) 6
c) 3
d) 4
Answer: b
Clarification: nth term of the AP is 7n – 9
Tn = 7n – 1
T1 = 7(1) – 1 = 6
The first term of AP is 6.
4. If the nth term of the AP is 8n + 1, then the 20th term will be ______
a) 160
b) 120
c) 161
d) 121
Answer: c
Clarification: nth term of the AP is 8n + 1
Tn = 8n + 1
T20 = 8(20) + 1
T20 = 161
5. What will be the 99th term from the end of the AP 500, 489, 478, 467… – 1139?
a) 1078
b) 1123
c) 12
d) 61
Answer: d
Clarification: In this case since we have to find the 99th term from the end.
We will consider the first term to be -1139 and the common difference will be 11
Now, a = -1139, d = 11 and n = 99
T99 = a + (n – 1)d
T99 = -1139 + (99 – 1)11
T99 = -1139 + 1078 = -61
The value of 99th term from the end is 61.
6. If the pth term of an AP is q and its qth term is p, then what will be the value of its (p + q)th term?
a) 1
b) p + q – 1
c) 0
d) 2(p + q – 1)
Answer: c
Clarification: pth term = q
a + (p – 1)d = q
a + pd – d = q (1)
qth term = p
a + (q – 1)d = p
a + qd – d = p (2)
Subtracting (2) from (1) we get,
a + qd – d – (a + pd – d) = p – q
qd – pd = p – q
d = -1
Substituting in equation 1, we get,
a = p + q – 1
(p + q)th term = a + (n – 1)d = p + q – 1 + (p + q – 1)(-1) = p + q – 1 – p – q + 1 = 0
7. If 5 times the 5th term of an AP is equal to 15 times its 15th term, then the value of its 20th term will be _______
a) 0
b) 1
c) 2
d) 3
Answer: a
Clarification: 5(5th term) = 15(15th term)
5th term = a + (5 – 1)d = a + 4d
15th term = a + (15 – 1)d = a + 14d
5(a + 4d) = 15(a + 14d)
5a + 20d = 15a + 210d
20d – 210d = 15a – 5a
-190d = 10a
a = -19d
Now, the 20th term = a + (20 – 1)d = a + 19d
But a = -19d
Hence, -19d + 19d = 0
8. If the 11th term of an AP is (frac {1}{13}) and its 13th term is (frac {1}{11}), then what will be the value of 143th term?
a) (frac {1}{143})
b) 1
c) 0
d) (frac {23}{143})
Answer: b
Clarification: Here 11th term = (frac {1}{13})
13thterm = (frac {1}{11})
Let the first term of the AP be a and common difference be d
T11 = a + (n – 1)d = (frac {1}{13})
T11 = a + (11 – 1)d = (frac {1}{13})
T11 = a + 10d = (frac {1}{13}) (1)
T13 = a + (n – 1)d = (frac {1}{11})
T13 = a + (13 – 1)d = (frac {1}{11})
T13 = a + 12d = (frac {1}{11}) (2)
Subtracting (1) from (2)
We get,
a + 12d – (a + 10d) = (frac {1}{11} – frac {1}{13})
2d = (frac {2}{143})
d = (frac {1}{143})
Now, substituting value of d in equation 1
We get,
T11 = a + 10((frac {1}{143})) = (frac {1}{13})
a = (frac {1}{143})
The 143th term = (frac {1}{143}) + 142(frac {1}{143} = frac {(1+142)}{143} ) = 1
9. If the 7th term of an AP is 20 and its 11th term is 40 then, what will be the common difference?
a) 3
b) 4
c) 5
d) 2
Answer: c
Clarification: Here 7th term = 20
11thterm = 40
Let the first term of the AP be a and common difference be d
T7 = a + (n – 1)d = 20
T7 = a + (7 – 1)d = 20
T7 = a + 6d = 20 (1)
T11 = a + (n – 1)d = 40
T11 = a + (11 – 1)d = 40
T11 = a + 10d = 40 (2)
Subtracting (1) from (2)
We get,
a + 10d – (a + 6d) = 40 – 20
4d = 20
d = 5
10. What will be the 14th term of the AP 5, 8, 11, 14, 17…….?
a) 30
b) 41
c) 40
d) 44
Answer: d
Clarification: Here a = 5, d = 8 – 5 = 3 and n = 14
T14 = a + (n – 1)d
T14 = 5 + (14 – 1)3
T14 = 5 + 13 × 3
T14 = 44