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Question

Question 15
If sum of the 3rd and the 8th terms of an AP is 7 and the sum of the 7th and 14th terms is -3, then find the 10th term.

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Solution

Let the first term, common difference of an AP are a and d, respectively.
According to the question,
a3+a8=7 and a7+a14=3
a+(31)d+a+(81)d=7 [ an=a+(n1)d]
And a + (7 - 1)d + a + (14 - 1)d = - 3
a + 2d + a + 7d = 7
And a + 6d + a + 13d =-3
2a + 9d = 7 . . . . . . . (i)
And 2a + 19d = - 3 . . . . . . . (ii)
On subtracting eq. (i) from eq.(ii), we get;
10d=10d=1
2a + 9 (-1) = 7
2a - 9 = 7
2a = 16 a = 8
a10=a+(101)d
= 8 + 9(-1)
= 8 - 9 = -1

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