CBSE Class 10 Mathematics Arithmetic Progression Assignment Set 13

Question. Find the Sum of the series
\( 1 + 4 + 7 + \dots \dots 25 \text{ terms} \)
Answer: 925

Question. Find the Sum of \( 15 \) terms of the following series
\( 36, 31, 26, \dots \dots \dots \)
Answer: 15

Question. Find the Sum of all two digit natural numbers, which are divisible by \( 3 \)
Answer: 1665

Question. How many terms of the A.P. \( 1, 3, 5, \dots \) are needed to give the Sum \( 256 \)?
Answer: 16

Question. How many terms of the A.P. \( -6, -\frac{11}{2}, -5, \dots \) are needed to give the Sum \((-25)\)? Also explain the reason for double answer.
Answer: \( 5, 20 \)
Since sum of first five terms = sum of \( 20 \) terms = \(-25\)
\(\therefore\) Sum of terms from \( 6 \) to \( 20 \) is zero.

Question. Find A.P. whose Sum to \( n \) terms is \( (2n^2 + n) \)
Answer: \( 3, 7, 11, 15, \dots \)

Question. Find the Sum to \( 17 \) terms of the sequence whose \( n^{\text{th}} \) term is given by \( t_n = 5n - 4 \)
Answer: 697

Question. Find the Sum of first \( 100 \) natural numbers.
Answer: 5050

Question. Find the Sum of all natural numbers between \( 250 \) and \( 1000 \) Which are exactly divisible by \( 3 \).
Answer: 156375

Question. The first term of an A.P. is \( 2 \) And the last term is \( 59 \). Find the Common difference if the Sum of all the terms is \( 610 \).
Answer: 3