Arithmetic Progressions
NIOS · Class 10 · Maths
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See them allFind whether the sequence 2, 7, 12, 17, 22, ... is an AP. If yes, find a and d.
Answer
Step 1: Find consecutive differences. 7 - 2 = 5 12 - 7 = 5 17 - 12 = 5 22 - 17 = 5 Step 2: The difference is constant, so it is an AP. Step 3: First term a = 2 and common difference d = 5. Answer: It …
Find whether the sequence 3, 7, 12, 18, 25, ... is an AP.
Answer
Step 1: Find consecutive differences. 7 - 3 = 4 12 - 7 = 5 18 - 12 = 6 25 - 18 = 7 Step 2: The differences are not the same. Answer: It is not an AP.
Find the nth term of the AP 5, 9, 13, 17, ...
Answer
Step 1: Identify a and d. a = 5, d = 4 Step 2: Use the nth term formula. tn = a + (n - 1)d Step 3: Substitute values. tn = 5 + (n - 1)4 Step 4: Simplify. tn = 5 + 4n - 4 = 4n + 1 Answer: tn = 4n + 1.
Find the 15th term of the AP 16, 11, 6, 1, -4, ...
Answer
Step 1: Identify a and d. a = 16, d = 11 - 16 = -5 Step 2: Use tn = a + (n - 1)d. Step 3: Substitute n = 15. t15 = 16 + (15 - 1)(-5) Step 4: Simplify. t15 = 16 + 14(-5) = 16 - 70 = -54 Answer: The 15t…
The first term of an AP is -3 and the 12th term is 41. Find the common difference.
Answer
Step 1: Use tn = a + (n - 1)d. Step 2: Substitute a = -3, n = 12, t12 = 41. 41 = -3 + (12 - 1)d 41 = -3 + 11d Step 3: Solve. 44 = 11d d = 4 Answer: The common difference is 4.
The common difference of an AP is 5 and the 10th term is 43. Find the first term.
Answer
Step 1: Use tn = a + (n - 1)d. Step 2: Substitute t10 = 43, d = 5. 43 = a + (10 - 1)5 43 = a + 45 Step 3: Solve. a = 43 - 45 = -2 Answer: The first term is -2.
The first term of an AP is -2 and the 11th term is 18. Find the 15th term.
Answer
Step 1: Find d first. t11 = a + (11 - 1)d 18 = -2 + 10d 20 = 10d d = 2 Step 2: Find t15. t15 = a + (15 - 1)d t15 = -2 + 14(2) t15 = -2 + 28 = 26 Answer: The 15th term is 26.
Why is the nth term formula tn = a + (n - 1)d true?
Answer
An AP starts with a. Each next term adds the same difference d. 1st term: a 2nd term: a + d 3rd term: a + 2d 4th term: a + 3d So the nth term has added d exactly (n - 1) times. That gives tn = a + (n …
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