Question

if the sum of the 3rd and the 8th term of an AP is 7 and the sum of the 7th and 14thterms is -3, find the 10th term

Answer 1

Let the first term of the A .P be a.

Third term of A.P = a + 2d .
8 th term of A.P = a + 7 d .

Sum of 3rd and 8th terms = a + 2d + a +7d = 2a + 9d.
A.T.Q -> 2a + 9d = 7 ...eq(1)

7th term of A.P = a +6d
14 th term of A.P = a + 13 d .

Sum of 7th and 14 th terms = a+ 6d + a + 13d = 2a + 19d .

ATQ -> 2a + 19d =-3 ...eq(2)

Now eq(2)-eq(1)

2a+19d = -3
2a + 9d = 7
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10d = -10
d = -1 .

Substitute in equation(1)

2a + 9d = 7

2a -9 = 7

2a = 7+9

2a =16

a = 8 .

Now we have (a ,d ) = (8 ,-1)

Now,10 th term = a + (10-1)d

10 th term = 8 + 9( -1 )

10 th term = 8 - 9 = -1

Therefore , 10 th term of A .P = -1