Question

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

Answer 1

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 .

Answer 2

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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