Q1
Assertion (A): The sequence 2, 4, 6, 8, ... is an AP.
Reason (R): In an AP the difference between consecutive terms is constant.
Choose the correct option:
Reason (R): In an AP the difference between consecutive terms is constant.
Choose the correct option:
📝 SolutionThe differences are all 2, a constant, so the sequence is an AP (A true). R states the defining property of an AP and explains why A is true.
Q2
The sum of first 20 terms of the AP 1, 3, 5, 7, ... is:
📝 Solution$a = 1, d = 2$. $S_{20} = \frac{20}{2}[2(1) + 19(2)] = 10[2 + 38] = 10 \times 40 = 400$.
Q3
The 15th term of the AP $x, x+2, x+4, ...$ is:
📝 Solution$d = 2$. $a_{15} = x + (15-1)(2) = x + 28$.
Q4
If $S_n = n^2$, then the first term of the AP is:
📝 SolutionFirst term $a_1 = S_1 = 1^2 = 1$.
Q5
The middle term of the AP 5, 9, 13, ..., 41 is:
📝 Solution$a = 5, d = 4, a_n = 41$: $41 = 5 + (n-1)4$, so $n = 10$... check: $(n-1)4 = 36$, $n = 10$. With 10 terms there are two middle terms (5th and 6th): $a_5 = 21, a_6 = 25$, average 23. The 6-term-symmetric middle value is 23.
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Class 10 · Maths
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