Decide whether following sequence is an A.P., if so find `20^(th)` term of the progression.
-12,-5,2,9,16,23,30, …

Answer

The given sequence is an A.P. The 20th term of the A.P. is 121.

Explanation

Here,`a=t_(1)=-12, t_(2)=-5,t_(3)=2,t_(4)=9,`
`t_(5)=16,...`
`t_(2)-t_(1)=-5-(-12)=-5+12=7,`
`t_(3)-t_(2)=-2(-5)=2+5=7,`
`t_(4)-t_(3)=9-2=7,`
`t_(4)-t_(3)=9-2=7,`
The common difference = d = 7
`"….(A constant number)"`
`therefore` given sequence is an A.P.
`t_(n)=a+(n-1)d " "`...(Formula) ,
`thereforet_(20)=-12+(20-1)xx7 " "`...(Substituting the values)
`=-12+19xx7`
`=-12+133`