General Mathematics I — kadesh Past Questions

University of Ilorin MTH101: 20 questions.

Topics: Sequence and Series

1. The first term of an A.P is 7, the last term is 70, and the sum of terms is 385. Find the number of terms.
   1. 8
   2. 6
   3. 10
   4. 12
2. The first four terms of a G.P series are 2 and 2048 respectively. The sum of the series is 1024. Find the number of terms.
   1. 11
   2. 4
   3. 6
   4. 7
3. Find the Arithmetic mean of 4 and 18.
   1. 11
   2. 12
   3. 2
   4. 6
4. Insert three A.M between 19 and 35.
   1. 24, 27, 31
   2. 23, 27, 32
   3. 27, 24, 30
   4. 23, 27, 31
5. T2 of a G.P is 35 and the T4 is 875. Find the first term \( a \).
   1. 7
   2. 6
   3. 5
   4. 4
6. The first term of an A.P is 7, the last term is 70, and the sum is 385. Find the number of terms and the common difference.
   1. n = 10 and d = 7
   2. n = 7 and d = 10
   3. n = -7 and d = 10
   4. n = 7 and d = -10
7. Find the sum of the first 10 terms of the G.P \( \frac{1}{8}, \frac{1}{4}, \frac{1}{2}, \dots \).
   1. 1025/8
   2. 527/8
   3. 548/8
   4. 610/8
8. A sequence in which each term is obtained by the addition of a constant number is called...
   1. AP
   2. GP
   3. GM
   4. AM
9. The third term of a G.P is 63 and the 5th term is 567. Find the sum of the first 6 terms.
   1. 2550
   2. 2548
   3. 2540
   4. 255
10. The sum of the nth term of a GP for \( r < 1 \) is given as...
    1. \( \frac{a(1 - r^n)}{1 - r} \)
    2. \( \frac{a(1 - r^n)}{r - 1} \)
    3. \( \frac{1 - r^n}{1 - r} \)
    4. \( \frac{a(1 - r^n)}{r} \)
11. The 4th term of an AP is 15, the 9th term is 35. Find the 15th term.
    1. 56
    2. 57
    3. 58
    4. 59
12. Find the 40th term of the linear sequence 6, 11, 16, 21.
    1. 200
    2. 201
    3. 202
    4. 203
13. If 8, x, y, z, and 20 are in AP, find x, y, and z.
    1. x = 11, y = 14, z = 17
    2. x = 10, y = 13, z = 16
    3. x = 14, y = 17, z = 11
    4. x = 17, y = 14, z = 10
14. Insert two Geometric means between 12 and 324.
    1. 36, 106
    2. 36, 108
    3. 37, 106
    4. 37, 108
15. If \( x+1, 2x-1, \) and \( x+5 \) are in A.P, find the value of \( x \).
    1. 4
    2. 9
    3. 16
    4. 8
16. Find three numbers in A.P whose sum is 3 and whose product is -15.
    1. 5, -1, -3
    2. 5, 1, -3
    3. -5, 1, 3
    4. 5, -1, 3
17. If \( x+2, x+3, \) and \( 2x^2 + 1 \) are 3 consecutive terms of an A.P, find the possible values of \( x \).
    1. 1/2 or 3/4
    2. ±3/2
    3. ±3/2 or -1
    4. ±1/2
18. What is the 2nd geometric mean if there are 3 geometric means between 2 and 32?
    1. 8
    2. 4
    3. 2
    4. 16
19. The sum of the first eight terms of a G.P is five times the sum of the first four terms. Find the common ratio.
    1. \( \sqrt[4]{4} \)
    2. 2
    3. 1/2
    4. 0
20. The formula to find the sum of an A.P is...
    1. \( S_n = \frac{n}{2}(a + (n-1)d) \)
    2. \( S_n = \frac{n}{2}[2a + (n-1)d] \)
    3. \( S_n = \frac{n}{2}(2a + n(a + 1)d) \)
    4. None of these

Register free to unlock all 20 questions with answers and explanations