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Arithmetic Progression (AP): Calculation based/Proofs
Ex 9.2, 7 Important Deleted for CBSE Board 2023 Exams
Ex 9.2, 8 Deleted for CBSE Board 2023 Exams
Ex 9.2, 13 Deleted for CBSE Board 2023 Exams
Example 4 Deleted for CBSE Board 2023 Exams
Ex 9.2, 5 Important Deleted for CBSE Board 2023 Exams
Misc 1 Deleted for CBSE Board 2023 Exams
Ex 9.2, 10 Deleted for CBSE Board 2023 Exams
Ex 9.2, 12 Deleted for CBSE Board 2023 Exams
Ex 9.2, 11 Important Deleted for CBSE Board 2023 Exams
Misc 15 Deleted for CBSE Board 2023 Exams
Misc 16 Important Deleted for CBSE Board 2023 Exams
Arithmetic Progression (AP): Calculation based/Proofs
Last updated at Oct. 7, 2021 by Teachoo
Example 5, If the sum of n terms of an A.P. is nP + 1/2n(n 1)Q , where P and Q are constants, find the common difference. Let a1, a2, an be the given A.P Given, Sum of n terms = nP + 1/2 n (n 1) Q Sn = nP + 1/2 n (n 1) Q Putting n = 1 in (1) S1 = 1 P + 1/2 1 (1 1)Q S1 = P + 1/2(0) S1 = P But sum of first 1 terms will be the first term a1 = S1 = P Sn = nP + 1/2 n (n 1) Q (1) Putting n = 2 in (1) S2 = 2P + 1/2 2(2 1)Q S2 = 2P + 1/2 2 1 Q S2 = 2P + Q Sum of first two terms = First term + Second term S2 = a1 + a2 S2 a1 = a2 a2 = S2 a1 Putting a1 = P , S2 = 2P + Q a2 = 2P + Q P = 2P P + Q = P + Q Thus, a2 = P + Q Common difference (d) = a2 a1 = (P + Q) P = Q Hence, common difference of the given A.P. is Q