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.

Answer

The 10th term of the given A.P. is -1.

Explanation

Let the first term A.P. be a and the common difference d.
`t_(n)=a+(n-1)d` …(Formula)
`thereforet_(3)=a+(3-1)d`
`thereforet_(3)=a+2d` …(1)
`t_(8)=a+(8-1)d`
`thereforet_(8)=a+7d " "...(2)`
`thereforet_(3)+t_(8)=a+2a+a+7d=7` ...[From (1),(2) and gievn ]
`thereforet_(3)+t_(8)=2a+9d=7` ...(3)
Similarity `t_(7)+t_(14)=-3` ...(Given)
`thereforea+(7-1)d+a+(14-1)d=-3`
`thereforea+6d+a+13d=-3`
`therefore2a+19d=-3 " "...(4)`
Substracting (3) from (4),
`2a+19d=-3" "...(4)`
`2a+9d=7" "...(3)`
`(---)/(10d=-10)`
`therefored=-1`
Substituting `d=-1`in equation(3),
`2a+9(-1)=7`
`therefore2a-9=7" "therefore2a=7+9`
`therefore2a=16" "thereforea=8`
Now, `a=8 and d=-1`
We want to find the 10th term.
`t_(n)=a+(n-1)d` ...(Formula)
`thereforet_(10)=8+(10-1)xx(-1)` ...(Substituting the values)
`=8+(9)xx(-1)`
`=8-9`
`thereforet_(10)=-1.`