CBSE Class 10 Mathematics Arithmetic Progression Assignment Set 10

Question. The sum to \( n \) terms of the series \( 1 + 2 + 3 + \dots + n \) is
(a) \( \frac{n(n+1)}{2} \)
(b) \( \frac{n+1}{2} \)
(c) \( \frac{n(n-1)}{2} \)
(d) \( \frac{n}{2} \)
Answer: (a) \( \frac{n(n+1)}{2} \)

Question. The general term of \( a, a+d, a+2d, \dots \) is
(a) \( a + (n+1)d \)
(b) \( a + (n-1)d \)
(c) \( n + (a-1)d \)
(d) None of the options
Answer: (b) \( a + (n-1)d \)

Question. The Sum to \( n \) terms of series \( a, a+d, a+2d, \dots \) is
(a) \( \frac{n}{2}[2a + (n+1)d] \)
(b) \( \frac{n}{2}[a - l] \)
(c) \( \frac{n}{2}[a + l] \)
(d) \( \frac{n}{2}[a + (n-1)d] \)
Answer: (c) \( \frac{n}{2}[a + l] \)

Question. \( 50^{\text{th}} \) term of \( 1, 3, 5, \dots \)
(a) \( 96 \)
(b) \( 97 \)
(c) \( 98 \)
(d) \( 99 \)
Answer: (d) \( 99 \)

Question. If \( x, y, z \) are in A.P then
(a) \( y = \frac{x+z}{2} \)
(b) \( x = \frac{y+z}{2} \)
(c) \( z = \frac{x+y}{2} \)
(d) \( y = \frac{x-z}{2} \)
Answer: (a) \( y = \frac{x+z}{2} \)

Question. Three special numbers of A-P are
(a) \( a, a-d, a+d \)
(b) \( a-d, a, a+d \)
(c) \( a-d, a+d, a \)
(d) \( a, a+d, a-d \)
Answer: (b) \( a-d, a, a+d \)

Question. \( n^{\text{th}} \) term of the sequence \( 1^2, 3^2, 5^2, 7^2, \dots \)
(a) \( n^2 \)
(b) \( (n+1)^2 \)
(c) \( (2n-1)^2 \)
(d) \( (2n+1)^2 \)
Answer: (c) \( (2n-1)^2 \)

Question. Sum of first \( 10 \) natural numbers starting from \( 48 \)
(a) \( 500 \)
(b) \( 515 \)
(c) \( 520 \)
(d) \( 525 \)
Answer: (d) \( 525 \)

Question. If \( a_n = 2n + 1 \), then \( a_{r-1} \) is
(a) \( 2r - 1 \)
(b) \( 2r + 1 \)
(c) \( 2r - 2 \)
(d) \( 2r + 2 \)
Answer: (a) \( 2r - 1 \)

Question. If \( a_n = \frac{(-1)^n + (3)^n}{n-1} \), 3rd term of this sequence is
(a) \( 15 \)
(b) \( 13 \)
(c) \( 11 \)
(d) \( 9 \)
Answer: (b) \( 13 \)

Question. In an AP, what does \( (t_n - t_{n-1}) \) represent?
(a) \( 3d \)
(b) \( 2d \)
(c) \( d \)
(d) \( -d \)
Answer: (c) \( d \)

Question. If in an AP, \( a=3, d=-1 \), then \( 50^{\text{th}} \) term will be
(a) \( 46 \)
(b) \( 45 \)
(c) \( -45 \)
(d) \( -46 \)
Answer: (d) \( -46 \)

Question. Which term of AP \( 1, 6, 11, 16, \dots \) is \( 81 \)?
(a) \( 17 \)
(b) \( 18 \)
(c) \( 19 \)
(d) \( 20 \)
Answer: (a) \( 17 \)

Question. If \( n^{\text{th}} \) term of an AP is \( 3n+2 \), what will be its \( 4^{\text{th}} \) term
(a) \( 15 \)
(b) \( 14 \)
(c) \( 13 \)
(d) \( 12 \)
Answer: (b) \( 14 \)

Question. \( t_{m+n} + t_{m-n} = \) how many times \( t_m \)
(a) \( 1 \)
(b) \( 2 \)
(c) \( 3 \)
(d) \( 4 \)
Answer: (b) \( 2 \)