the 5th term of an A.P. is 8. The 8th term exceeds three times the 2nd term by 2 . find the first term, the common difference and the sum of first 15 term
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a+4d=8 (equation 1)
a+7d=2+{3(a+d)}
a+7d=2+3a+3d
a+7d-3a-3d=2
-2a+4d=2
d=2+2a/4
=2(1+a)/4
=1/2(a+1)
Putting the value of d in equation 1
a+4d=8
a+4{1/2(a+1)=8
a+2(a+1)=8
a+2a+2=8
3a=8-2=6
a=6/3
a=2
d=1/2(a+1)
=1/2(2+1)
=1/2×3
=3/2
n=15
Sn=n/2[2a+(n-1)d]
=15/2[2×2+(15-1)3/2]
=15/2[4+(14×3/2)]
=15/2[4+21]
=15/2×25
=375/2
a+7d=2+{3(a+d)}
a+7d=2+3a+3d
a+7d-3a-3d=2
-2a+4d=2
d=2+2a/4
=2(1+a)/4
=1/2(a+1)
Putting the value of d in equation 1
a+4d=8
a+4{1/2(a+1)=8
a+2(a+1)=8
a+2a+2=8
3a=8-2=6
a=6/3
a=2
d=1/2(a+1)
=1/2(2+1)
=1/2×3
=3/2
n=15
Sn=n/2[2a+(n-1)d]
=15/2[2×2+(15-1)3/2]
=15/2[4+(14×3/2)]
=15/2[4+21]
=15/2×25
=375/2
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