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.

Explanation

Let the first term and common difference of an AP are a and d, respectively.
According to the question,
`a_(3)+a_(8)=7` and `a_(7)+a_(14)= -3`
`implies a+(3-1)d+a+(8-1)d=7 " " [:.a_(n)=a+(n-1)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= -10 impliesd= -1 " " ` [ from Eq. (i)]
`2a+9(-1)=7`
` implies2a-9=7`
`2a=16impliesa=8`
` :. a_(10)=a+(10-1)d`
` " " =8+9(-1)`
` " " =8-9= -1`