Question -
Answer -
Given:
600 and 700 radio setsunits are produced in third and seventh year respectively.
a3┬а=600 and a7┬а= 700
(╤Ц)┬аThe production in thefirst year
We need to find theproduction in the first year.
Let first yearproduction be тАШaтАЩ
So the AP formed is,a, a+x, a+2x, тАж.
By using the formula,
an┬а= a+ (n-1)d
a3┬а= a+ (3-1)d
600 = a + 2d тАж. (i)
a7┬а= a+ (7-1)d
700 = a + 6d
a = 700 тАУ 6dтАж. (ii)
Substitute value of ain (i) we get,
600 = a + 2d
600 = 700 тАУ 6d + 2d
700 тАУ 600 = 4d
100 = 4d
d = 100/4
= 25
Now substitute valueof d in (ii) we get,
a = 700 тАУ 6d
= 700 тАУ 6(25)
= 700 тАУ 150
= 550
тИ┤ The production in thefirst year, тАШaтАЩ is 550
(╤Ц╤Ц)┬аthe total product inthe 7 years
We need to find thetotal product in 7 years i.e. is S7
By using the formula,
Sn┬а=n/2 [2a + (n-1)d]
n = 7, a = 550, d = 25
S7┬а=7/2 [2(550) + (7-1)25]
= 7/2 [1100 + 150]
= 7/2 [1250]
= 7 [625]
= 4375
тИ┤ The total product inthe 7 years is 4375.
(╤Ц╤Ц╤Ц)┬аthe product in the 10th┬аyear.
We need to find theproduct in the 10th┬аyear i.e. a10
By using the formula,
an┬а= a+ (n-1)d
n = 10, a = 550, d =25
a10┬а=550 + (10-1)25
= 550 + (9)25
= 550 + 225
= 775
тИ┤ The product in the 10th┬аyearis 775.