Answer :

Given, a_{3} = 600 and a_{7} = 700

Let the first term be a and common difference be d.

Since, nth term an AP is given by :

a_{n} = a + (n - 1)d

Where,

a = First term of AP

d = Common difference of AP

and no of terms is ‘n’

⇒ a_{3} = a + (3 - 1)d

⇒ 600 = a + 2d … (i)

⇒ a_{7} = a + (7 - 1)d

⇒ 700 = a + 6d …(ii)

On solving eq. (i) and (ii), we get :

a = 550 and d =25

∴ production in first year a_{1} = a 550

and production in tenth year a_{10}

= a + (10 - 1)d

= 550 + 9 × 25

= 550 + 225 = 775

∴ a_{10} = 775

Since the sum of n terms is

S_{n =} _{}Total production in first seven year S_{7}

S_{7 =}

S_{7} = 3.5 × [ (2× 550) + (6 × 25)]

S_{7} = 3.5 × [ 1100 + 150]

S_{7} = 3.5 × 1250

S_{7} = 4375

Hence, (i) the production in the 1^{st} year is 550

(ii) the production in the 10^{th} year is 775

(iii) the total production in first 7 years is 4375.

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