Arithmetic Progressions — Class 10 solved problems

38 problems from this chapter, each solved step by step.

'A thief runs away from a police station with a uniform speed of 100 m/minute. After exactly one minute, a policeman runs after the thief to catch him. The poli
The policeman will catch the thief after 5 minutes.
If the sum of the first m terms of an AP is the same as the sum of its first n terms (m ≠ n), show that the sum of its first (m + n) terms is: S_m+n = 0
S_m+n = 0
Find the 20th term of the AP 7, 11, 15, 19,...
The 20th term of the AP is 83.
A school has decided to plant some endangered trees on 51^(st) World Environment Day in the nearest park. They have decided to plant those trees in few concentr
(i) 230 trees (ii) 60 trees (iii) (a) 16 rows OR (b) 1550 trees
Two A.P.s have the same first term. The common difference of the first A.P. is -3 and of the second A.P. is -5. The difference of the 6^(th) term of the second
10
If k + 7, 2k - 2 and 2k + 6 are three consecutive terms of an A.P., then the value of k is
The value of k is 17.
(a) Find the sum of all integers between 50 and 500, which are divisible by 7. OR (b) How many numbers lie between 10 and 300, which when divided by 4 leave a r
The sum of all integers between 50 and 500, which are divisible by 7, is 17696.
If x, 2x + 9, 4x + 3 are three consecutive terms of an A.P., then the value of x is:
The value of x is 15.
(a) Find the sum of all multiples of 9 lying between 300 and 700. OR (b) The 26^(th), 11^(th) and the last term of an A.P. are 0, 3 and -51 respectively. Find t
The common difference is -(1)/(5) and the number of terms is 281.
Which term of the AP: 21, 18, 15,... is – 81? Also, is any term 0?
The 35 -th term of the AP is -81. Yes, 0 is the 8 -th term of the AP.
The roots of the quadratic equation 3x² - px + q = 0 are 10^(th) and 11^(th) terms of an arithmetic progression with common difference (3)/(2). If the sum of th
474
The number of terms of an A.P. is even; the sum of all the odd terms is 24, the sum of all the even terms is 30 and the last term exceeds the first by (21)/(2).
4
The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of the first sixteen terms of the AP.
The sum of the first sixteen terms of the AP is 76 or 20.
Find the sum of the first 20 terms of the AP: 5, 8, 11, 14, and so on.
The sum of the first 20 terms of the given AP is 670.
The first term of an A.P. is a, the second term is b and the last term is c. Show that the sum of the A.P. is ((b+c-2 a)(c+a))/(2(b-a)).
The sum of the A.P. is ((b+c-2 a)(c+a))/(2(b-a)).
In an A.P. the p th term is q and the (p+q)^ th term is 0. Then the q th term is (A) -p (B p (C) p+q (D) p-q
The q th term is p.
Determine the AP whose 3rd term is 5 and the 7th term is 9.
The Arithmetic Progression (AP) is 3, 4, 5, 6,
The 8th term of an A.P., whose first two terms are - 5 and 2 respectively, is:
The 8th term of the A.P. is 44.
Suppose that the number of terms in an A.P. is 2k, k N. If the sum of all odd terms of the A.P. is 40, the sum of all even terms is 55 and the last term of the
The value of k is 5.
Let the sequence a_n be defined as follows: a_1=1, a_n=a_n-1+2 for n ≥ 2. Find first five terms and write corresponding series.
The first five terms are 1, 3, 5, 7, 9. The corresponding series is 1 + 3 + 5 + 7 + 9.
Let a_1, a_2,, a_2024 be an Arithmetic Progression such that a_1 + (a_5 + a_10 + a_15 + + a_2020) + a_2024 = 2233. Then a_1 + a_2 + a_3 + + a_2024 is equal to:
11132
Let a_1,a_2,a_3, be in an A.P. such that Σ_k=1^(12)a_2k-1=-(72)/(5)a_1, a_1 0. If Σ_k=1^n a_k=0, then n is:
n=11
Find the sum of first 24 terms of the A.P. a_1, a_2, a_3, if it is known that a_1+a_5+a_10+a_15+a_20+a_24=225.
The sum of the first 24 terms of the A.P. is 900.
Which term of the AP: 21, 18, 15, is -81? Also, is any term 0? Give reason for your answer.
The 35th term of the AP is -81. Yes, 0 is a term of the AP, specifically the 8th term, because the calculated value of 'n' for a_n = 0 is a positive integer (n=
Let T_r be the r^(th) term of an A.P. If for some m, T_m = (1)/(25), T_25 = (1)/(20), and 20 Σ_r=1^(25) T_r = 13, then 5m Σ_r=m²m T_r is equal to
126
If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of the next four terms, then the sum of the first 20 term
-1080
Find the 10th term of the AP: 2, 7, 12,
The 10th term of the AP is 47.
Check whether 301 is a term of the list of numbers 5, 11, 17, 23,
No, 301 is not a term of the given list of numbers.
If there are (2 n+1) terms in an A.P., then prove that the ratio of the sum of odd terms and the sum of even terms is (n+1): n
The ratio of the sum of odd terms and the sum of even terms is (n+1): n.
The p^ th term of an A.P. is a and q^ th term is b. Prove that the sum of its (p+q) terms is (p+q)/(2)[a+b+(a-b)/(p-q)].
The sum of its (p+q) terms is (p+q)/(2)[a+b+(a-b)/(p-q)].
Show that (x²+x y+y²),(z²+x z+x²) and (y²+y z+z²) are consecutive terms of an A.P., if x, y and z are in A.P.
The given terms (x²+x y+y²),(z²+x z+x²) and (y²+y z+z²) are consecutive terms of an A.P.
Let S_n = (1)/(2) + (1)/(6) + (1)/(12) + (1)/(20) + up to n terms. If the sum of the first six terms of an A.P. with first term -p and common difference p is √(
25
In an arithmetic progression, if S_40 = 1030 and S_12 = 57, then S_30 - S_10 is equal to:
515
The product of three numbers in A.P. is 224, and the largest number is 7 times the smallest. Find the numbers.
The three numbers are 2, 8, and 14.
The 10th common term between the series 3+7+11+ and 1+6+11+ is (A) 191 (B) 193 (C) 211 (D) None of these
191
How many two-digit numbers are divisible by 3?
There are 30 two-digit numbers divisible by 3.
Ford owns a garden and he grows 40 roses every week. He supplies Roses to the local flower shops. The first flower shop orders 20 roses, the second flower shop
Ford lacks 100 roses to supply all the flower shops every month.
Let a_n be the n th term of an A.P. If S_n = a_1 + a_2 + + a_n = 700 for some n, a_6 = 7 and S_7 = 7, then a_n is equal to:
64

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