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Class 10 A - P

The document contains 13 questions related to arithmetic progressions (AP). The questions cover topics such as: - Proving relationships between different terms in an AP - Finding the sum of terms in an AP given information about individual terms - Determining properties of numbers or terms if they are in an AP - Relating characteristics of two or more APs The questions progressively increase in complexity, requiring proofs or multiple steps to solve.

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Angad
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656 views1 page

Class 10 A - P

The document contains 13 questions related to arithmetic progressions (AP). The questions cover topics such as: - Proving relationships between different terms in an AP - Finding the sum of terms in an AP given information about individual terms - Determining properties of numbers or terms if they are in an AP - Relating characteristics of two or more APs The questions progressively increase in complexity, requiring proofs or multiple steps to solve.

Uploaded by

Angad
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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2021-2022 CLASS 10 (2020-2021) (Subjective Worksheet)

ARITHMETIC PROGRESSIONS
Q. 1 If 9th term of an A.P. is zero, prove that the 29th term is double the 19th
term?

Q. 2 If a1, a2, a3…….a24 are in AP, a1 + a5 + a10 + a15 +a20 + a24 =30 then

Find a1 + a2 + a3 +…….a24 .

Q.3 Interior angles of a polygon are in A.P. If the smallest angle is 120 ° and

common difference is 5°, find the number of sides of the polygon.

Q. 4 If (a)2,(b)2,(c)2 are in A.P., then show that : , are in A.P.

Q. 5. Find the sum of the first 30 terms of an A.P., whose nth term is 2–3n.

Q. 6 If mth and nth terms of an A.P. are 1/n and1/m respectively, then

find the sum of mn terms

Q.7 If the pth, qth & rth term of an AP is x, y and z respectively,

show that x(q-r) + y(r-p) + z(p-q) = 0

Q. 8. If the roots of the equation a(b – c) x2 + b(c – a) x + c (a – b) = 0 are


equal, then show that 1/a , 1/b , 1/c are in A.P.

Q. 9. If Sn denotes the sum of first n terms of an A.P.,

Prove that S12 =3(S8 – S4)

Q.10. If , are in A.P. then show that (b−c)2,(c−a)2,(a−b)2 are in A.P.

Q. 11. The sum of four consecutive numbers in A.P. is 32 and the ratio of the
product of the first and last terms to the product of two middle terms is 7 : 15.
Find the number

Q. 12. The ratio of sum to n terms of two A.P.’S is 3n + 4 5n + 6. Then find


the ratio of their 15 th terms.

Q .13.If pth term of an A.P. 1/q and qth term is 1/p. prove that the sum of the first ‘
pq’ terms is 1/2(pq +1).

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