Arithmetic Progressions
Gujarat Board · Class 10 · Mathematics
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Find the 10th term of the arithmetic progression: 3, 7, 11, 15, ...
The sum of the first 15 terms of an AP with first term 4 and common difference 3 is:
If the 7th term of an AP is 20 and the 12th term is 35, find the first term:
A ladder has rungs that decrease in length uniformly. If the bottom rung is 50 cm and each successive rung is 2 cm shorter, what is the length of the 8th rung from the bottom?
Sample Questions
Which of the following sequences are arithmetic progressions? (Select all correct answers)
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2, 5, 8, 11, 14, ..., 10, 7, 4, 1, -2, ..., 5, 5, 5, 5, 5, ...
For a sequence to be an AP, the difference between consecutive terms must be constant. Option 1: d = 3 (AP), Option 2: differences are 3,5,7,9 (not AP), Option 3: d = -3 (AP), Option 4: d = 0 (AP), Option 5: differences are 2,4,8,16 (not AP).
Find the number of terms in the AP: 7, 10, 13, ..., 43
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13
Given: a = 7, d = 3, last term = 43. Using an = a + (n-1)d: 43 = 7 + (n-1)×3. Solving: 43 - 7 = (n-1)×3, so 36 = (n-1)×3, thus n-1 = 12, therefore n = 13.
The sum of first n natural numbers 1 + 2 + 3 + ... + n is:
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n(n+1)/2
Natural numbers 1, 2, 3, ..., n form an AP with a = 1, d = 1. Using S = n/2[2a + (n-1)d]: S = n/2[2×1 + (n-1)×1] = n/2[2 + n - 1] = n/2[n + 1] = n(n+1)/2.
Which of the following are correct statements about arithmetic progressions? (Select all correct answers)
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The common difference can be negative, The common difference can be zero, The nth term formula is an = a + (n-1)d
The common difference d can be positive, negative, or zero. An AP can have any number of terms (finite or infinite). The nth term formula an = a + (n-1)d is correct. Terms in an AP can be positive, negative, or zero.
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