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Applications of A.P

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Ex. (1) A mixer manufacturing company manufactured 600 mixers in 3rd year and in 7th year they manufactured 700 mixers. If every year there is same growth in the production of mixers then find (i) Production in the first year (ii) Production in 10th year (iii) Total production in first seven years.

Solution : Addition in the number of mixers manufactured by the company per year is constant therefore the number of production in successive years is in A.P.

(i) Let’s assume that company manufactured tn mixers in the nth year then as per

given information,

t_{3} = 600, t_{7} = 700

We know that t_{n}= a+(n-1)d

t_{3}= a+(3-1)d

a + 2d = 600. . . (I)

t_{7}= a+(7-1)d

t_{7}= a+6d = 700

a+2d = 600

∴ Substituting a = 600 - 2d in equation (II),

600 - 2d + 6d = 700

4d = 100

∴ d = 25

a+2d = 600

∴ a + 2 ×25 = 600

a + 50 = 600

∴ a = 550

∴ Production in first year was 550.

(ii) t_{n}= a+(n-1)d

t_{10}= 550+(10-1) × 25

= 550 + 225

Production in 10th year was 775.

(iii) For finding total production in first 7 years let’s use formula for Sn.

`S_n =n/2 [2a+(n-1)d]`

`S_n =7/2 [1100 + 150] =7/2 [1250] = 7 xx 625 = 4375`

Total production in first 7 years is 4375 mixers.