arith metic progression questions
Answers
Answer:
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Step-by-step explanation:
1. The 7th term of an AP is -39/12 and the 15th term is -103/12. What is the 27th term?
A. -187/12B. -191/12C. -199/12D. -205/12
Sol : Option C
The 7th term is a + 6d = -39/12
The 15th term is a + 14d = -103/12
Equating these terms with their values and solving as simultaneous equations, we get a = 3/4 and d = – 2/3.So the 27th term is (a + 26d) = 3/4 + (-52/3) = -199/12.
2. In an AP of 21 terms, the sum of the first 3 terms is – 33 and that of the middle 3 is 75. What is the sum of the AP?
A. -955B. -1155C. 525D. 715
Sol : Option C
The AP can be expressed as a, (a + d), ---, (a +20d). The sum of the first 3 terms is (3a + 3d) = -33 and the sum of the middle 3 terms is (3a + 30d) = 75. Solving these two equations, we get a = -15 and d = 4. The sum of the 1st 21 terms is (21/2) (2 * -15 + 20 * 4) = 525.
Q.3. The 6th term of an AP is 6 and the 16th term is 14. What is the 27th term?
A. 106/5B. 22/5C. 118/5D. 114/5
Sol : Option D
The 6th term is a + 5d = 6
The 16th term is a + 15d = 14
Equating these terms with their values and solving as simultaneous equations, we get a = 2 and d = 4/5. So the 27th term is (a + 26d) = 2 + (104/5) = 114/5.
Q.4. In an AP, the ratio of the 2nd term to the 7th term is 1/3. If the 5th term is 11, what is the 15th term?
A. 28B. 31C. 33D. 36
Sol : Option B
The 2nd and the 7th terms are (a + d) and (a + 6d) respectively. The ratio of these terms is 1/3. Solving this ratio, we get 2a = 3d. The 5th term is (a + 4d) = 11. Substituting for a, we get a = 3 and d = 2. Therefore, the 15th term is (a + 14d) = 31.
Q.5. The sum of the first 3 terms in an AP is 6 and that of the last 3 is 16. If the AP has 13 terms, what is the sum of the middle three terms?
A. 7B. 9C. 11D. 13
Sol : Option C
The AP can be expressed as a, (a + d), ---, (a +12d). The sum of the first 3 terms is (3a + 3d) = 6 and that of the last 3 is (3a + 33d) = 16. Solving these equations, we get a = 5/3 and d = 1/3. The sum of the middle 3 terms is (3a + 18d) = 11.