Test 05 || Class 10th Maths || Ch. 05 Arithmetic progression (समांतर श्रेणी) (SOI)

Test 05 || Class 10th Maths || Ch. 05 Arithmetic progression

1. If p,q, r and s are in AP then what is r - q.

2. If 1/a, 1/b and 1/c are in AP so that b = 2ac/(a + c).

(Also writes in inverse from)

3. If p,q, r are in AP then what is (p - q)/ (q - r).

4. If SN denotes the sum of n terms of an ap then show the value of S(n + 3) - 3S(n + 2) + 3 S(n + 1) - Sn = 0.

5. If (P + Q)th term of an AP is m and (P - Q)th term is n then each term is.?        [(m+n)/2]

S₁₂

6. if SN denotes the sum of the first n term of an ap whose common difference is d then show that Sn -  2S(n -1) + S(n -2)= d.

7. What will be the next term of the sequence 1/(1 + √x), 1/(1 + x), 1/(1 - √x) is ? 

8. If the numbers a, b, c, d, e form an AP then the value of a - 4 b + 6 c - 4d + e is ?       [0]

9. If the sum of n terms of an AP is the same as the sum of its n terms then the sum of its (m + n) term is ?                                  [0]

10. In an AP if S₂₁ = 1250 and S₂₀ =1200, find a₂₁a.

11. Solve 1 + 6 + 11 + .... + 6 = 2148

13. If a, b, c are in AP show that 1/(√b + √c), 1/(√c + √a), 1/(√a + √b), are in AP.

13. If a², b², c² are in AP show that 1/(b + c), 1/(c + a), 1/(a + b), are in AP.

14. Prove that no matter what the real numbers a and b are the sequence with nth term (a+ nb) is always an AP. What is the common difference? what is sum of the first 20 terms?

15. Derive the formula for the sum of first n terms of an AP, whose first term is a and the common difference is d.

16. the sum of n, 2n, 3n terms of an AP are S₁, S₂, S₃ respectively prove that S₃ = 3 ( S_{2 –}S₁).                                                       

17. The ratio of the sum of m and n terms of an AP is m² :  n².  Show that the ratio of mth and nth term is (2m - 1) : (2n -1).