Question 1 :
In an AP, given $d = 5, S_9 = 75$, find a and $a_9$.
Question 2 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc9273b230584979a16.JPG' />
In the above fig. A ladder has rungs 25 cm apart. The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and the bottom rungs are $2\frac{1}{2}$ m apart, what is the length of the wood required for the rungs?
Question 3 :
In an AP, given $a = 8, a_n = 62, S_n = 210$, find n and $d$.
Question 4 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc8273b230584979a15.JPG' />
In the above fig. In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line. A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?
Question 5 :
If the sum of the first n terms of an AP is $4n – n^2$, what is the first term (that is $S_1$)?
Question 7 :
In an AP, given $a_3 = 15, S_{10} = 125$, find d and $a_{10}$.
Question 8 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 10th term ?
Question 9 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc7273b230584979a14.JPG' />
In the above fig. 200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on. In how many rows are the 200 logs placed and how many logs are in the top row?
Question 10 :
How many terms of the AP : 9, 17, 25, . . . must be taken to give a sum of 636?
Question 11 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the nth term ?
Question 12 :
Subba Rao started work in 1995 at an annual salary of Rs. 5000 and received an increment of Rs. 200 each year. In which year did his income reach Rs. 7000?
Question 13 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc3273b230584979a0e.JPG' />
In the above fig, find the missing value corresponding to (iii)
Question 14 :
Check whether – 150 is a term of the AP : 11, 8, 5, 2 . . .
Question 15 :
Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
Question 16 :
Find the sum of the following AP: $\frac{1}{15}, \frac{1}{12}, \frac{1}{10}, . .$ , to 11 terms
Question 17 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 3rd term ?
Question 18 :
Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.
Question 19 :
The sum of the third and the seventh termsof an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.
Question 20 :
Find the sum of the following AP: 7 + 10.5 + 14 + . . . + 84
Question 21 :
Find the sum of the following AP: 2, 7, 12, . . ., to 10 terms.
Question 22 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc4273b230584979a10.JPG' />
In the above fig, find the missing value corresponding to (i)
Question 23 :
In the following AP, find the missing term: 2, __ ,26
Question 24 :
In an AP, given $a = 2, d = 8, S_n = 90$, find n and $a_n$.
Question 25 :
The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x.
Question 26 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc6273b230584979a13.JPG' />
In the above fig. A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, . . . as shown in above figure. What is the total length of such a spiral made up of thirteen consecutive semicircles?
Question 27 :
In an AP, given a = 5, d = 3, $a_n$= 50, find n and $S_n$.
Question 28 :
For what value of n, are the nth terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?
Question 29 :
Ramkali saved Rs. 5 in the first week of a year and then increased her weekly savings by Rs. 1.75. If in the nth week, her weekly savings become Rs. 20.75, find n.
Question 30 :
11th term of the AP: – 3, -0.5, 2, . . ., is
Question 31 :
Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.
Question 33 :
Find the 20th term from the last term of the AP : 3, 8, 13, . . ., 253.
Question 34 :
Find the sum of the following AP: 34 + 32 + 30 + . . . + 10
Question 35 :
Which term of the AP : 3, 15, 27, 39, . . . will be 132 more than its 54th term?
Question 36 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc9273b230584979a17.JPG' />
A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete. Each step has a rise of 0.25 m and a tread of 0.5 m. Calculate the total volume of concrete required to build the terrace.
Question 37 :
30th term of the AP: 10, 7, 4, . . . , is
Question 38 :
If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum offirst n terms.
Question 39 :
If the 3rd and the 9th terms of an AP are 4 and – 8 respectively, which term of this AP is zero?
Question 40 :
In an AP, given $a = 7, a_{13} = 35$, find d and $S_{13}$.
Question 41 :
In an AP, given l = 28, S = 144, and there are total 9 terms. Find a.
Question 42 :
A sum of Rs. 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. 20 less than its preceding prize, find the smallest value of the prize.
Question 43 :
The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
Question 44 :
Find the sum of the following AP: –37, –33, –29, . . ., to 12 terms.
Question 45 :
The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, what is the sum of the AP?
Question 46 :
Does $a_1, a_2, . . ., a_n, . . $ form an AP where $a_n = 3 + 4n$?
Question 47 :
In an AP, given $a = 3, n = 8, S = 192$, find d.
Question 48 :
Find the sum of the following AP: –5 + (–8) + (–11) + . . . + (–230)
Question 49 :
Which term of the AP : 121, 117, 113, . . ., is its first negative term?
Question 50 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 2nd term ?
