Arithmetic and Geometric Progression
ICSE · Class 10 · Mathematics
Flashcards for Arithmetic and Geometric Progression — ICSE Class 10 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Explore the full setFind the common difference and the first four terms of the A.P. with first term a = 7 and d = 3.
Answer
Step 1: Use the A.P. form a, a+d, a+2d, a+3d. Step 2: Substitute a = 7 and d = 3. Step 3: Terms are 7, 10, 13, 16. Answer: Common difference = 3; first four terms = 7, 10, 13, 16.
Solve: Find the 8th term of the A.P. 4, 9, 14, 19, ...
Answer
Step 1: Identify a = 4 and d = 9 - 4 = 5. Step 2: Use T_n = a + (n-1)d. Step 3: T_8 = 4 + (8-1)5 = 4 + 35 = 39. Answer: T_8 = 39.
Find the 12th term of the A.P. where a = 6 and d = -2.
Answer
Step 1: Use T_n = a + (n-1)d. Step 2: T_12 = 6 + (12-1)(-2). Step 3: T_12 = 6 + 11(-2) = 6 - 22 = -16. Answer: T_12 = -16.
Find the common difference of the A.P. 15, 11, 7, 3, ...
Answer
Step 1: Use d = T_n - T_(n-1). Step 2: d = 11 - 15 = -4. Step 3: Check: 7 - 11 = -4 and 3 - 7 = -4. Answer: d = -4.
Find the last term l of an A.P. with a = 5, d = 4, and n = 10.
Answer
Step 1: Use l = a + (n-1)d. Step 2: l = 5 + (10-1)4. Step 3: l = 5 + 36 = 41. Answer: l = 41.
Find the 6th term from the end of an A.P. with last term l = 50 and d = 3.
Answer
Step 1: Use nth term from the end = l - (n-1)d. Step 2: 6th term from the end = 50 - (6-1)3. Step 3: 50 - 15 = 35. Answer: 35.
Three numbers are in A.P. and their sum is 24. Find the numbers using the standard selection method.
Answer
Step 1: For three numbers in A.P. with given sum, take them as a-d, a, a+d. Step 2: Their sum is (a-d) + a + (a+d) = 3a. Step 3: 3a = 24, so a = 8. Step 4: Numbers are 8- d, 8, 8+ d. Since no d is giv…
If three numbers a, b, c are in A.P. and a = 5, c = 17, find b.
Answer
Step 1: Use the condition for three numbers in A.P.: 2b = a + c. Step 2: 2b = 5 + 17 = 22. Step 3: b = 22/2 = 11. Answer: b = 11.
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