Question

The fifth and tenth terms of an A.P. are 8 and -7 respectively. Find the 100th and 500th terms of the A.P.
Can someone please solve this for me, possibly showing all necessary steps?

Answer 1

see u are having the 5th and 10th term...
so, 8 = a + (n-1)d here n = 5
-7 = a + (n-1)d. here n = 10..
now u have 2 variables i.e. "a" nd "d" .... and 2 equations... solve them and proceed

Answer 2

Thank you :) I figured it out. Sorry for the trouble.

Answer 3

In an Arithmetic Sequence the difference between one term and the next is a constant.
\[xn = a + d(n-1) \]The fifth and tenth terms of an A.P. are 8 and -7 respectively.
\[a+d(5-1)=8 \]\[a+d(10-1)=-7 \]\[a+4d=8 \]\[a+9d=-7 \]\[ 4d-9d=8--7 \], \[-5d=15 \],\[d=-3 \]\[a+4(-3)=8 \]\[ a-12=8 \]\[a=20 \]
\[20+-3(100-1)= \]\[20+-3(500-1)= \]