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Question

If sum of 3rd and 8th terms of an A.P. is 7 and sum of 7th and 14th terms is –3 then find the 10 th term .

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Solution

It is given that,
a3 + a8 = 7
a7 + a14 = –3

Now,
an=a+n-1da3+a8=7a+3-1d+a+8-1d=7a+2d+a+7d=72a+9d=72a=7-9d ...1a7+a14=-3a+7-1d+a+14-1d=-3a+6d+a+13d=-32a+19d=-37-9d+19d=-3 from 17+10d=-310d=-3-710d=-10d=-12a=7-9-1 from 12a=7+92a=16a=8

Now,
a10=a+10-1d =8+9-1 =8-9 =-1

Hence, the 10th term is –1.

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