In an A.P., the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20th term is -112.

Answer

N/a

Explanation

Hera a= 2
`"Sum of first 5 terms "=(1)/(4)xx "sum of next 5 terms"`
`rArr" "S_(5)=(1)/(4)(S_(10)-S_(5))`
`rArr" "4cdotS_(5)=S_(10)-S_(5)`
Sequence and Series
`rArr" "5cdotS_(5)=S_(10)`
`rArr" "5xx(5)/(2)[2a+4d]=(10)/(2)[2a+9d]`
where d= common difference
`rArr" "5(2a+4d)=2(2a+9d)`
`rArr" "6a=-2d`
`rArr" "6xx2=-2d`
`rArr" "d=-6`
`"Now "T_(20)=a+19d`
`rArr" "T_(20)=2+19xx(-6)`
`=2-114=-112.`