Arithmetic progression and geometric progression - One Line Questions
1.
If a, b, c are in AP, then b is the arithmetic mean of a and c. The value of b is: —
(a+c)/2
2.
In an AP, the m-th term is n and the n-th term is m. What is the (m+n)-th term? —
-(m+n)
3.
In an AP, the sum of the first p terms is equal to the sum of the first q terms. Then the sum of the first (p+q) terms is: —
0
4.
The sum of the first 15 terms of an AP is 255, and the common difference is 2. What is the first term? —
1
5.
The sum of the first 4 terms of a GP is 40, and the common ratio is 3. What is the first term? —
2
6.
The sum of the first 3 terms of a GP is 39/10. If the common ratio is 3/2, find the first term. —
1
7.
If the sum of the first n terms of a GP is 3^n - 1, then the common ratio is: —
3
8.
If the sum of the first n terms of a GP is 5(2^n - 1), what is the common ratio? —
2
9.
The sum of the first 10 terms of an AP is 120. If the first term is 3, find the common difference. —
2
10.
If the first term of a GP is 1, and the sum to infinity is 2, what is the common ratio? —
1/2
11.
If the first term of a GP is 1, and the sum of the first three terms is 7/4, find the common ratio. —
1/2
12.
The sum of the first 20 terms of an AP is 400 and the sum of the first 40 terms is 1600. Find the sum of the first 10 terms. —
100
13.
In a geometric progression (GP), the first term is 2 and the common ratio is 3. What is the 5th term? —
162
14.
Which term of the AP 2, 5, 8, ... is 59? —
20th
15.
If the 3rd term of an AP is 10 and the 7th term is 22, what is the common difference? —
3
16.
The sum of the first n terms of an AP is given by S_n = 2n^2 + 3n. What is the common difference? —
4
17.
If the 2nd term of a GP is 6 and the 4th term is 54, what is the common ratio? —
3
18.
The sum of the first 5 terms of a GP is 31, and the sum of the first 10 terms is 1023. What is the common ratio? —
2
19.
The 4th term of an AP is 11 and the 7th term is 20. What is the 1st term? —
2
20.
The sum of the first 6 terms of a GP is 9 times the sum of the first 3 terms. What is the common ratio? —
3
21.
The sum of the first n terms of a GP is 2(3^n - 1). What is the common ratio? —
3
22.
If the product of three terms in GP is 216, and the sum of their squares is 156, find the terms. —
3, 6, 12
23.
If the nth term of a GP is 3n, then the common ratio is: —
3
24.
The sum of the first n terms of an AP is 3n^2 - n. What is the common difference? —
6
25.
The sum of the first n terms of an AP is given by S_n = (3n+1)n. Find the common difference. —
6
26.
The sum of three terms in AP is 21. If the product of the first and third term is 65, find the terms. —
3, 7, 11
27.
In an arithmetic progression (AP), the first term is 5 and the common difference is 3. What is the 10th term? —
29
28.
The sum of the first n terms of a GP is given by S_n = 4(3^n - 1). What is the first term? —
8
29.
The sum of the first n terms of an AP is S_n. If S_{2n} = 3S_n, then find the ratio S_{3n}/S_n. —
6
30.
Find the geometric mean of 4 and 9. —
6
31.
The sum of an infinite GP is 15, and the sum of the squares of its terms is 45. Find the first term. —
10
32.
The first term of an AP is -15, and the sum of the first 6 terms is 15. What is the common difference? —
5
33.
The sum of the first n terms of an AP is 3n^2 + 5n. Find the n-th term. —
6n - 2
34.
The sum of the first 10 terms of an AP is 100 and the sum of the first 20 terms is 400. Find the sum of the first 30 terms. —
900
35.
What is the sum of the first 8 terms of the GP 3, 6, 12, ...? —
759
36.
If the sum of n terms of an AP is an^2 + bn, then the common difference is: —
2a
37.
In a GP, if the first term is a and the common ratio is r, the sum of the first n terms is: —
a(r^n - 1)/(r-1)
38.
If a, b, c are consecutive terms of a GP, then: —
b^2 = ac
39.
If a, b, c are in AP, then b-a is equal to: —
c-b
40.
If a, b, c are in GP, then b/a is equal to: —
c/b
41.
In an AP, the sum of terms equidistant from the beginning and end is: —
Equal to the sum of the first and last term
42.
In an AP, if the first term is a and the common difference is d, the sum of the first n terms is: —
n/2 * [2a + (n-1)d]
43.
If the sum of the first n terms of a GP is S_n, and the sum of the first 2n terms is S_{2n}, then the sum of the first 3n terms is: —
S_{3n} = S_{2n} + (S_{2n} - S_n)^2 / S_n
44.
If the sum of the first n terms of an AP is S_n, then the n-th term is given by: —
S_n - S_{n-1}
45.
The sum of the first n terms of a GP is S_n. If the common ratio is r, then the n-th term is given by: —
S_n - S_{n-1} * r
46.
If the sum of n terms of an AP is S_n, and the sum of m terms is S_m, then the ratio of their m-th and n-th terms is: —
(2n-1)/(2m-1)
47.
If a, b, c are in GP, then b is the geometric mean of a and c. The value of b is: —
sqrt(ac)
48.
In a GP, if the p-th term is x and the q-th term is y, then the r-th term is: —
x^((q-r)/(q-p)) * y^((p-r)/(q-p))
49.
If x, y, z are in AP, then x+z is equal to: —
2y
50.
If x, y, z are in GP, then xz is equal to: —
y^2