the sum of the fourth term and seventh term of an ap is 5 and their product is 7 find the sum of first n terms of the AP Please answer quickly with full explanation!!!!!!
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Step-by-step explanation:
Fourth term of AP= a+ 3d.................….(1)
seventh term of AP= a+6d....…..…......(2)
given
S4+S7= 5 =>. (a+3d) + ( a+6d) = 5. from (1) and (2)
=>. 2a+9d= 5=>. a= (5-9d)/2.........................(3)
again. S4×S7= (a+3d) ( a+6d)= 7
a²+9ad+18d² =. 7 .......(4)
substituting value of a in (4) and after simplify
3d²-1=0=> d= ±1/3
substituting in(3)
a= (5-9×1/3)/2= =1. for positive value of d
a= ( 5+9×1/3)/2= 4 for negative value of d
therefore
sum of 1st n terms Sn= n/2[ ( 2a+ (n-1)d]
case 1=> a= 1, d= 1/3
. Sn= n/2[ 2×1+(n-1) ( 1/3)
=. (n+5)n/6
case2=> a= 4. d= -1/3
Sn= n/2[2×4+(n-1)(-1/3)]
=( 25-n)/6
fou
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