Arithmetic Progression — Flashcards
Maharashtra Board · Class 10 · Mathematics
25 flashcards for Arithmetic Progression (Maharashtra Board Class 10 Mathematics) to test yourself on key terms and facts.
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Find the next three terms of the A.P. 100, 70, 40, 10, ...
Answer
Step 1: Find the common difference. 70 - 100 = -30 40 - 70 = -30 So, d = -30. Step 2: Add -30 to the last term. 10 + (-30) = -20 -20 + (-30) = -50 -50 + (-30) = -80 Answer: The next three terms are -2…
Check whether 4, 4, 4, 4, ... is an A.P. If yes, find d.
Answer
Step 1: Find the difference between consecutive terms. 4 - 4 = 0 4 - 4 = 0 Step 2: The difference is constant. So this is an A.P. Step 3: Common difference d = 0. Answer: Yes, it is an A.P. and d = 0.
Find the common difference of the A.P. -1, -1.5, -2, -2.5, ...
Answer
Step 1: Subtract the first term from the second. -1.5 - (-1) = -0.5 Step 2: Check again. -2 - (-1.5) = -0.5 -2.5 - (-2) = -0.5 Answer: The common difference is d = -0.5.
Is 1^3, 2^3, 3^3, 4^3, ... an A.P. or a G.P. ?
Answer
Step 1: Write the terms. 1, 8, 27, 64, ... Step 2: Check differences. 8 - 1 = 7 27 - 8 = 19 64 - 27 = 37 The differences are not constant. Step 3: Check ratios. 8/1 = 8 27/8 is not 8 The ratios are no…
Solve: Find the 100th term of the A.P. 5, 8, 11, 14, ...
Answer
Step 1: Identify the values. a = 5, d = 3, n = 100 Step 2: Use the nth term formula. t_n = a + (n - 1)d Step 3: Substitute. t_100 = 5 + (100 - 1)3 = 5 + 99 x 3 = 5 + 297 = 302 Answer: The 100th term i…
When do you use t_n = a + (n - 1)d? Show with the A.P. 14, 16, 18, ...
Answer
Use this formula when you know the first term, common difference, and the term number. For 14, 16, 18, ... a = 14, d = 2 Find the 5th term: t_5 = 14 + (5 - 1)2 = 14 + 8 = 22 Answer: Use t_n = a + (n -…
Find the 15th term of an A.P. with first term 70 cm and common difference 10 cm.
Answer
Step 1: Use the nth term formula. t_n = a + (n - 1)d Step 2: Substitute the values. a = 70 cm, d = 10 cm, n = 15 Step 3: Calculate. t_15 = 70 + (15 - 1)10 = 70 + 140 = 210 cm Answer: The 15th term is …
Kabir's height was 70 cm at 1 year, 80 cm at 2 years, and 90 cm at 3 years. If the pattern continues as an A.P., what is his height at 15 years?
Answer
Step 1: Identify the A.P. 70, 80, 90, ... Step 2: Find the common difference. 80 - 70 = 10 cm Step 3: Use t_n = a + (n - 1)d. a = 70 cm, d = 10 cm, n = 15 Step 4: Substitute. t_15 = 70 + (15 - 1)10 = …
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