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Answers
Answer:
550
775
4375
Step-by-step explanation:
given
No of manufactured TV sets in third year is=600
No of manufactured TV sets in seventh year is=700
a)find the production in 1st year
by using AP
T3=600
T7=700
nth term=a+(n-1)d
T3=a+(3-1)d=a+2d=600 (equation 1)
T7=a+(7-1)d=a+6d= 700 (equation 2)
subtract equation 1 and equation 2
a+2d=600
a+6d=700
- - -
-4d=-100
d=-100/-4
d=25
substitute it in equation 1
a+2*25=600
a+50=600
a=550
550 TV sets are manufactured in 1st year
b)the production in the 10th year
a=550
d=25
nth term=a+(n-1)d
10th term=550+(10-1)25
=550+9*25
=550+225
=775
775 TV sets are manufactured in 10th year
c)the total no of TV sets produced in 7 years
a=625
d=25
n=7
sum of n terms in an AP=n/2(2a+(n-1)d
the total no of TV sets produced in 7 years = 7/2(2*550+(7-1)25)
=7/2(1100+150)
=7/2(1250)
=7*650
=4375
total 4375 TV sets are produced in 7 years