In an ap the first term is 2 and the sum of first five term is one forth of the next five terms . Show that 20th term is -112?
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a=2
a20=a+19d=-112........1
2+19d=-112
19d=-112-2
d=-114/19=-6
s5=5/2[2×2+(5-1)-6
=5/2(4-24)
=5/2(-20)
=5×-10
s5 =-50
s10=10/2[2×2+(10-1)-6
=5(4-54)
=5×-50=-250
next 5 terms sum=-250-(-50)
=-250+50
=-200
next 5 terms sum(1/4)=(first 5 terms sum)
-200×1/4=-50
-50=-50
a20=a+19d=-112........1
2+19d=-112
19d=-112-2
d=-114/19=-6
s5=5/2[2×2+(5-1)-6
=5/2(4-24)
=5/2(-20)
=5×-10
s5 =-50
s10=10/2[2×2+(10-1)-6
=5(4-54)
=5×-50=-250
next 5 terms sum=-250-(-50)
=-250+50
=-200
next 5 terms sum(1/4)=(first 5 terms sum)
-200×1/4=-50
-50=-50
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