# A manufacture of

Given, a3 = 600 and a7 = 700

Let the first term be a and common difference be d.
Since, nth term an AP is given by :
an = a + (n - 1)d

Where,

a = First term of AP
d = Common difference of AP
and no of terms is ‘n’

a3 = a + (3 - 1)d
600 = a + 2d … (i)

a7 = 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 a1 = a 550
and production in tenth year a10
= a + (10 - 1)d
= 550 + 9 × 25
= 550 + 225 = 775
a10 = 775

Since the sum of n terms is
Sn =

Total production in first seven year S7
S7 =

S7 = 3.5 × [ (2× 550) + (6 × 25)]
S7 = 3.5 × [ 1100 + 150]
S7 = 3.5 × 1250
S7 = 4375

Hence, (i) the production in the 1st year is 550
(ii) the production in the 10th year is 775
(iii) the total production in first 7 years is 4375.

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