Question

the sixth term of an ap is -10 and 10th term is,-16 determine the AP

Answer 1

I hope this will help you..



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Answer 2

nth term of an A.P. is given by,

$a_{n} = a + (n - 1)d$
Where 'a' is the first term and 'd' is the common difference.

Now,

$a_{6} = a + 5d = - 10 \\ a_{10} = a + 9d = - 16$
Subtract the first equation from the second,

$4d = - 6 \\ d = - \frac{3}{2}$
Put this value of d in any one equation to get
$a = - \frac{5}{2}$
Therefore the A.P is a, a+d, a+2d....

$- \frac{5}{2}, - 4, - \frac{11}{2} .....$