the sum of the first term and fifth term term of an ascending AP is 26 and the product of the second term by fourth term is 160 find the sum of the first term seven terms of this AP
maaa:
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Answered by
44
Heya!
First term = a
Fifth term =a+(5-1)d=a+4d
Sum of First term& Fifth terms =a+a+4d=2a+4d
ATQ --> 2a+4d=26
a+d=13
Fourth term =a+(4-1)d=a+3d
Second term = a+d
Product of Second & Fourth terms =(a+3d)(a+d)=160
13(a+3d)=160
a+3d=160/13
Now we have
a+d=8
a+3d=160/13
Sum of first & seven terms =a+a+6d =2a+6d=2(a+3d) =2(160/13)=320/13
.
Sum of first & seven terms is 320/13 .
First term = a
Fifth term =a+(5-1)d=a+4d
Sum of First term& Fifth terms =a+a+4d=2a+4d
ATQ --> 2a+4d=26
a+d=13
Fourth term =a+(4-1)d=a+3d
Second term = a+d
Product of Second & Fourth terms =(a+3d)(a+d)=160
13(a+3d)=160
a+3d=160/13
Now we have
a+d=8
a+3d=160/13
Sum of first & seven terms =a+a+6d =2a+6d=2(a+3d) =2(160/13)=320/13
.
Sum of first & seven terms is 320/13 .
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Answered by
36
a+a5=26
a+a+4d=26
2a+4d=26
a+2d=13--(1)
a4*a2=160
(a+3d)*(a+d)=160
(a+2d+d)*(a+2d-d)=160
(13+d)*(13-d)=160
13²-d²=160
169-d²=160
d²=9
d=3
a+2d=13(from eq.1)
a+2(3)=13
a=13-6
a=7
S7=n/2(2a+(n-1)d)
=7/2(2(14)+(7-1)3)
=7/2(28+(6)3)
=7/2(28+18)
=7/2(46)
=7*23
=161
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