If the sum of first 7 terms of an ap is 49 and that of 17thterm is 289 find the sum of find the sum of first n terms
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Answer:
SUM OF 7 TERM = 49
SO,
49 = N/2 [2A+(N-1)D]
==> 49 = 7/2 [2A+(7-1)D]
==> 49×2/7 = 2A+6D
==> 7×2 = 2(A+D)
==> 7×2 / 2 = A+D
==> 7 = A+D ...(1)
SUM OF 17TH TERM = 289
==> 289 = 17/2 [2A+(17-1)D]
==> 289×2/17 = 2A+16D
==> 17×2 = 2(A+8D)
==> 17×2/2 = A+8D
==> 17 = A+8D...(2)
SO, FROM EQ(2) AND EQ(1)
==> A+D = 7
A+8D = 17
==> -7D = -10
==> D = 10/7
PUTTING VALUE OF D IN EQ(1)
==> A+D = 7
==> A+10/7 = 7
==> A = 7-10/7
==> A = 49-10/7
==> A = 39/7
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