CBSE Class 10 Arithmetic Progressions Sure Shot Questions Set 12

Question. Find the common difference \( d \) of the A.P. 10, 8, 6, 4, 2 ........
Answer: -2

Question. If 7th and 6th terms of an A.P. are 25 and 32, what is the value of \( d \)?
Answer: -7

Question. Find the 6th term of an A.P. 3, 5, 7......
Answer: 13

Question. 1, 4, 7, 10, 13 ...... is an A.P. Find ‘d’.
Answer: 3

Question. Find the common difference of the A.P. –1, 2, 5, 8, 11, .......
Answer: 3

Question. What is the common difference of the A.P. formed by even numbers?
Answer: 2

Question. Find the value of 11th term of the A.P., whose first two terms are –3 and 4.
Answer: 67

Question. If \( t_n = 2n + 1 \) then find the series.
Answer: 3, 5, 7,.....

Question. If \( a_2 = 5 \) and \( a_3 = 9 \), then find \( t_5 \).
Answer: 17

Question. Find the nth term of the A.P. 5, 2, –1, –4, –7, ....... .
Answer: \( 8 - 3n \)

Question. What is the difference between 3rd and 8th terms of the A.P? 3, 7, 11, 15, .......
Answer: 20

Question. If first term of an A.P. is 3 and 11th term is 43, find the common difference.
Answer: 4

Question. If 4th and 8th terms of an A.P. are 11 and 23 respectively, find a and d.
Answer: a = 2, d = 3

Question. First term of an A.P. is –2 and 10th term is 28. What is the value of d (common difference)
Answer: \( \frac{10}{3} \)

Question. Find the 16th term of an A.P. if a = 15, and d = –2
Answer: -15

Question. Find 8th term of an A.P. whose 3rd term is –5 and common difference is 4.
Answer: 15

Question. Which term of an A.P. 3, 7, 11, 15, ...... will be 20 more than its 6th term?
Answer: 11th

Question. How many d’s will be added to get 29th term of an A.P. to the first term?
Answer: 28

Question. Find 4th term from the end of the A.P. –4, –1, 2, 5, 8, 11, 14, 17, 20, ........ 54.
Answer: 45

Question. The sum of series in A.P. is 128. If the first term is 2 and the last term is 14 find the number of terms of the series.
Answer: 16

Question. Find the value of d of the A.P. whose nth term is 9 – 5n.
Answer: -5

Question. If a = 5, d = –1, then which term of the A.P. is zero?
Answer: 6

Question. How many multiples of 4 lies between 10 and 250?
Answer: 60

Question. Find the sum of first 5 terms of the A.P. 3, 7, 11.......
Answer: 55

Question. If \( S_n \) and \( S_{n-1} \) are given, then what is \( S_n - S_{n-1} \)?
Answer: \( t_n \)

Question. Find the 10th term of the A.P. 117, 104, 91, 78, .......
Answer: 0

Question. If common difference of an A.P. is 5, find the difference of 15th and 11th terms.
Answer: 20

Question. What should be added to 184 to become the term of the sequence 3, 7, 11,.......?
Answer: 3

Question. If 7th term of an A.P. is 32 and 13th term is 62. Find the series.
Answer: 2, 7, 12, ......

Question. Find the number of terms of the A.P. 5, 9, 13, 17, 21, 25, 29, ...... 41
Answer: 10

Question. Find the number of terms of the A.P. 1, 4, 7, 10, ...... 61.
Answer: 21

Question. If Rajni goes from Rohini to Lajpat Nagar with a speed of 30km/hr by car and after every hour she increases the speed by 5km/hr., then what is the speed of car after 4 hours?
Answer: 50km/hr.

Question. Find the sum of all terms of the A.P. 1 + 3 + 5 + ....... + 29.
Answer: 225

Question. Find the sum of first 10 natural numbers.
Answer: 55

Question. What is the sum of first five multiples of 3?
Answer: 45

Question. Find the sum 2 + 6 + 10 + 14 + ....... + 34.
Answer: 162

Question. Find the sum of 2 + 4 + 6 + ...... up to n terms.
Answer: \( n(n + 1) \)

Question. If three consecutive terms of an A.P. are a – d, a, a + d and their sum is 54 and d is 7, find the three terms.
Answer: 11, 18, 25

Question. Find the A.P. if the 15th term is 10 more than the 13th term and first term is 5.
Answer: 5, 10, 15, .....

Question. Determine the sum of first 10 terms if an A.P. if \( t_2 = 2 \) and \( t_7 = 22 \).
Answer: 160

Question. Determine ‘k’ so that 8k + 4, 6k – 2, 2k – 7 are three consecutive terms of an A.P.
Answer: \( \frac{1}{2} \)

Question. If the sum of first ‘n’ term of an A.P. is \( 3n^2 + 2n \), then find its nth terms.
Answer: \( 6n - 1 \)

Question. For the A.P. –9, –14, –19, –24 find \( t_{30} - t_{20} \).
Answer: -50

Question. If 7th term of an A.P. is zero then what is the relation between 17th and 37th term?
Answer: Thrice

Question. If the 9th term of an A.P. is zero, then what is the ratio of 29th term to 19th term?
Answer: 2 : 1

Question. A man saved Rs. 16,500 in 10 years. In each year after the first he saved Rs. 100 more than he did in the preceeding year. How much did he save in the first year?
Answer: Rs. 1200

Question. Find the sum of first 100 multiples of 5.
Answer: 25250

Question. Find the sum of the A.P. 1 + 3 + 5 + 7 + ..... + 199.
Answer: 10,000

Question. Find the value of k if the kth term of the A.P. –1, –3, –5, –7..... is –151.
Answer: 76

Question. The sum of n terms of a series is \( (n^2 + 2n) \) for all values of n. Find the 3rd term of the series.
Answer: 7