10th Mathematics _ Arithmetic Progression Important PYQs
Arithmetic Progression IMPORTANT PYQs Part 1 Question 1-5
The sum of first and eighth terms of an A.P. is 32 and their product is 60. Find the first term and common difference of the A.P. Hence, also find the sum of its first 20 terms.
In an A.P. of 40 terms, the sum of first 9 terms is 153 and the sum of last 6 terms is 687. Determine the first term and common difference of A.P. Also, find the sum of all the terms of the A.P.
Find the number of terms of the A.P. : 293, 285, 277,… , 53
For what value of 'n', are the nth terms of the A.P's: 9,7,5,.... and 15, 12, 9,.... the same?
Determine the A.P. whose third term is 5 and seventh term is 9.
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Arithmetic Progression IMPORTANT PYQs Part 2 Question 6-10
Which term of the progression 20,19 1/4,18 1/2,17 3/4 ,... is the first negative term?
Find the middle term of the A.P. 213, 205, 197,....., 37
The sum of the 5th and the 9th terms of an A.P. is 30. If its 25th term is three times its 8th term, find the A.P.
In Mathematics, relations can be expressed in various ways. The matchstick patterns are based on linear relations. Different strategies can be used to calculate the number of matchsticks used in different figures. One such pattern is shown below. Observe the pattern and answer the following questions using Arithmetic Progression: (a) Write the AP for the number of triangles used in the figures. Also, write the nth term of this AP. (b) Which figure has 61 matchsticks?
In an A.P., if S5 + S7 = 167 and S10 = 235, then find the A.P., where Sn denotes the sum of its first n terms.
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Arithmetic Progression IMPORTANT PYQs Part 3 Question 11-15
Solve: 1 + 4 + 7 + 10 + ... + x = 287
Find the sum of all the two digit numbers which leave the remainder 2 when divided by 5.
If 7 times the seventh term of the AP is equal to 5 times the fifth term, then find the value of its 12th term.
Which term of the A.P. 27, 24, 21,.. is zero?
In an Arithmetic Progression, if d = 4, n = 7, a₁ = 4, then find a.
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Arithmetic Progression IMPORTANT PYQs Part 4 Question 16-20
If 7 times the seventh term of the AP is equal to 5 times the fifth term, then find the value of its 12th term.
The school auditorium was to be constructed to accommodate at least 1500 people. The chairs are to be placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one. (i) If the first circular row has 30 seats, how many seats will be there in the 10th row? (ii) For 1500 seats in the auditorium, how many rows need to be there? OR (ii) If 1500 seats are to be arranged in the auditorium, how many seats are still left to be put after 10th row? (iii) If there were 17 rows in the auditorium, how many seats will be there in the middle row?
Find how many integers between 200 and 500 are divisible by 8.
In an AP of 50 terms, the sum of the first 10 terms is 210 and the sum of its last 15 terms is 2565. Find the AP
The sum of four consecutive number in AP is 32 and the ratio of the product of the first and last term to the product of two middle terms is 7 : 15. Find the numbers.