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Question -

A manufacturer of the radio sets produced 600 units in the third year and 700 units in the seventh year. Assuming that the product increases uniformly by a fixed number every year, find
(╤Ц) the production in the first year
(╤Ц╤Ц) the total product in the 7 years and
(╤Ц╤Ц╤Ц) the product in the 10th year.



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.

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