1. The third term of an AP is 8 and 9th term of an AP exceeds 3times the third term by 2.find the sum of its first 19 terms
2. The sum of the third and seventh term of an AP is 6 and their product is 8. Find the sum of first 16 terms whose common difference is positive.
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Given that
a3=8
a+2d=8......(i)
a9=8-2
a9=6
a+8d=6....(ii)
Subtracting (i) from (ii),
6d=-2
d=-1/3
a=8+2/3
a=26/3
a19=23/3+18(-1/3)
=23/3-18/3
=5/3
S19=19/2[26/3+5/3]
=19/2(31/3)
=589/6
a3=8
a+2d=8......(i)
a9=8-2
a9=6
a+8d=6....(ii)
Subtracting (i) from (ii),
6d=-2
d=-1/3
a=8+2/3
a=26/3
a19=23/3+18(-1/3)
=23/3-18/3
=5/3
S19=19/2[26/3+5/3]
=19/2(31/3)
=589/6
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