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Showing 2 questions in Mathematics for Class 10. Tap a card to reveal the answer.
MathematicsArithmetic ProgressionseasyThe first term of an AP is 3 and the common difference is 5. Find its 10th term.
Reveal answer ↓
What it is
In an AP each term rises by a fixed step d; the nth term is a + (n - 1)d.
Answer
The nth term of an AP is a_n = a + (n - 1)d. Here a = 3, d = 5, n = 10, so a_10 = 3 + (10 - 1) x 5 = 3 + 45 = 48.
a_n = a + (n - 1)d
- •a_n = a + (n - 1)d
- •a = 3, d = 5, n = 10
- •a_10 = 48
Why learn this
APs model salaries with fixed raises, seating rows, EMIs and steady savings.
💡 Memory trick
nth term = start + (steps taken) x step = a + (n - 1)d.
MathematicsArithmetic ProgressionsmediumFind the sum of the first 20 terms of the AP 2, 5, 8, 11, ...
Reveal answer ↓
What it is
The sum of an AP pairs the first and last terms: S = n/2 [2a + (n - 1)d].
Answer
Here a = 2 and d = 3. The sum of n terms is S_n = n/2 [2a + (n - 1)d]. So S_20 = 20/2 [2(2) + 19(3)] = 10 [4 + 57] = 10 x 61 = 610.
S_n = n/2 [2a + (n - 1)d]
- •a = 2, d = 3, n = 20
- •S_n = n/2 [2a + (n-1)d]
- •S_20 = 10 x 61 = 610
Why learn this
It quickly totals things that grow steadily - savings, stacked logs, salaries over years.
💡 Memory trick
Sum = (number of terms / 2) x (2a + (n - 1)d): half the count times the bracket.