CBSE Class 10 Mathematics Arithmetic Progression Assignment Set 11

Fill the Gap

Question. The \(n^{\text{th}}\) term of \(1, 3, 5, \ldots\) is ____________
Answer: \(t_n = 2n - 1\)

Question. The \(4^{\text{th}}\) term of \(2, 4, \ldots\) is ____________
Answer: \(t_4 = 8\)

Question. The general term of \(a, a+d, a+2d, \ldots\) is ____________
Answer: \(t_n = a + (n-1)d\)

Question. The \(r^{\text{th}}\) term of \(x, x+y, x+2y, \ldots\) is ____________
Answer: \(t_r = x - y + ry\)

Question. The Sum to \(n\) terms of \(1, 2, 3, \ldots\) is ____________
Answer: \(S_n = \frac{n(n+1)}{2}\)

Question. If \(x, y, z\) are three numbers which are in AP then \(y = \_\_\_\_\_\_\_\_\_\)
Answer: \(y = \frac{x+z}{2}\)

Question. The Sum to \(n\) terms of AP \(a, a+d, \ldots\) is ____________
Answer: \(S_n = \frac{n}{2}[2a + (n-1)d]\)

Question. If \(t_n = 3n-2\), the series is ____________
Answer: \(1, 4, 7, \ldots\)

Question. The \(4^{\text{th}}\) term of the sequence \(a_n = n(n+2)\) is ____________
Answer: \(24\)

Question. Is the series \(1^2, 2^2, 3^2, 4^2, \ldots\) in AP ____________
Answer: No

Question. Form a series with first term \(a=5\) and \(c.d\) as \(3\) ____________
Answer: \(5, 8, 11, \ldots\)

Question. In \(S_n = \frac{n}{2}[a+l]\), the meaning of \(l\) is ____________
Answer: Last term

Question. What is most important to form an AP ____________
Answer: Common difference must be same

Question. \(12^{\text{th}}\) term of \(5, 8, \ldots\) is ____________
Answer: \(38\)

Question. \(S_n - S_{n-1} = \_\_\_\_\_\_\_\_\_\)
Answer: \(t_n\)