CBSE Class 10 Mental Maths Arithmetic Progressions Worksheet

Very Short Answer Type Questions

Question. For the AP : 0.6, 1.7, 2.8, 3.9, . . ., write the first term a and the common difference d.
Answer : a = 0.6, d = 1.1

Question. Ramkali saved Rs 5 in the first week of a year and then increased her weekly savings by ₹1.75. If in the n^th week, her weekly savings become ₹ 20.75, find n.
Answer : 10

Question. A sum of Rs 1000 is invested at 8% simple interest per year. Calculate the interest at the end of each year. Do these interests form an AP? If so, find the interest at the end of 30 years making use of this fact.
Answer : ₹ 2400

Question. An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29^th term.
Answer : 64

Question. Which term of the AP : 3, 15, 27, 39, . . . will be 132 more than its 54^th term?
Answer : 65^th term

Question. Two APs have the same common difference. The difference between their 100^th terms is 100, what is the difference between their 1000th terms?
Answer : 100

Question. The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
Answer : n = 16, d = 8/3

Question. The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?
Answer : n = 38, S = 6973

Question. Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
Answer : Sum = 1661

Question. Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.
Answer : S₅₁ = 5610

Question. Find the sum of the first 40 positive integers divisible by 6.
Answer : 4920

Question. Find the 10^th term of the AP : 2, 7, 12, . . .
Answer : 47

Question. How many three-digit numbers are divisible by 7?
Answer : 128

Question. The 7th term of an AP is – 4 and its 13th term is –16. Find the AP.
Answer : 8, 6, 4, 2, 0, …

Question. Find the common difference of an AP whose fi rst term is 5 and the sum of its first four terms is half the sum of the next four terms.
Answer : 1, 5, 9, 13, …

Question. The 9th term of an AP is –32 and the sum of its 11th and 13th terms is –94. Find the common difference of the AP.
Answer : –5

Question. The sum of the 2nd and the 7th terms of an AP is 30. If its 15th term is 1 less than twice its 8th term, find the AP.
Answer : 1, 5, 9, 13, …

Question. If 4 times the 4th term of an AP is equal to 18 times its 18th term then find its 22nd term.
Answer : 0

Question. The 19th term of an AP is equal to 3 times its 6th term. If its 9th term is 19, find the AP.
Answer : 3, 5, 7, 9, …

Question. For what value of n, the nth terms of the arithmetic progressions 63, 65, 67, … and 3, 10, 17, … are equal?
Answer : n = 13 12. Tn =(4n –1)

Question. The 4th term of an AP is 11. The sum of the 5th and 7th terms of this AP is 34. Find its common difference.
Answer : 3