CBSE Class 10 Mathematics Arithmetic Progression Assignment Set 17

Question. Form a A.P with first term is 5, and the common difference is 3
Answer: \( 5, 8, 11, \dots \)

Question. Write the next three terms in the following A.P.
\( 1, -1, -3, -5, \dots \)
Answer: \( -7, -9, -11 \)

Question. Write the general term and \( 5^{\text{th}} \) term of the series
\( \frac{1}{a}, \frac{1+2a}{a}, \frac{1+4a}{a}, \dots \)
Answer:
\( t_n = 2n + \left(\frac{1}{a} - 2\right) \)
\( t_5 = \frac{1}{a} + 8 \)

Question. Which term of the sequence \( 72, 70, 68, \dots \) is \( 40 \)?
Answer: \( 17^{\text{th}} \)

Question. Is the following sequence in AP?
(i) \( 0.3, 0.03, 0.003, \dots \)
(ii) \( \sqrt{2}, \sqrt{2}+1, \sqrt{2}+2, \sqrt{2}+3, \dots \)
Answer:
(i) No
(ii) Yes

Question. Write the common difference of the following AP
\( 0.5, 0.85, 1.20, 1.55, \dots \)
Answer: \( d = 0.35 \)

Question. The \( n^{\text{th}} \) term of a progression is \( 3n+1 \). Prove that it is an A.P. Find its \( 5^{\text{th}} \) term.
Answer: It is in AP because the Cd remains the same between two consecutive terms.

Question. How many terms are there in the following A.P.?
(i) \( 10, 13, 16, \dots 49 \)
(ii) \( 14 \frac{1}{2}, 12, \dots (-38) \)
Answer:
(i) 14
(ii) 22

Question. Which term of the AP is 320 in the series \( 5, 8, 11, \dots \)?
Answer: \( n = 106 \)

Question. Is 310 a term of the sequence \( 3, 8, 11, \dots \)?
Answer: No