Question

Q). 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
(і) the production in the first year
(іі)The total product in the 7 years and
(ііі) The product in the 10th year.


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Answer 1

Answer:

Given: 600 and 700 radio sets units are produced in third and seventh year respectively. a3 = 600 and a7 = 700 (і) The production in the first year We need to find the production in the first year. Let first year production be ‘a’ So the AP formed is, a, a + x, a + 2x, …. By using the formula, an = a + (n - 1)d a3 = a + (3 - 1)d 600 = a + 2d …. (i) a7 = a + (7 - 1)d 700 = a + 6d a = 700 – 6d…. (ii) Substitute value of a in (i) we get, 600 = a + 2d 600 = 700 – 6d + 2d 700 – 600 = 4d 100 = 4d d = 100/4 = 25 Now substitute value of d in (ii) we get, a = 700 – 6d = 700 – 6(25) = 700 – 150 = 550 ∴ The production in the first year, ‘a’ is 550 (іі) the total product in the 7 years We need to find the total product in 7 years i.e. is S7 By using the formula, Sn = n/2 [2a + (n - 1)d] n = 7, a = 550, d = 25 S7 = 7/2 [2(550) + (7 - 1)25] = 7/2 [1100 + 150] = 7/2 [1250] = 7 [625] = 4375 ∴ The total product in the 7 years is 4375. (ііі) the product in the 10th year. We need to find the product in the 10th year i.e. a10 By using the formula, an = a + (n-1)d n = 10, a = 550, d = 25 a10 = 550 + (10 - 1)25 = 550 + (9)25 = 550 + 225 = 775 ∴ The product in the 10th year is 775Read more on Sarthaks.com - https://www.sarthaks.com/802993/manufacturer-the-radio-sets-produced-600-units-the-third-year-and-700-units-the-seventh-year#:~:text=600%20and%20700%20radio%20sets,third%20and%20seventh%20year%20respectively.&text=We%20need%20to%20find%20the%20production%20in%20the%20first%20year.&text=So%20the%20AP%20formed%20is,%2C%20a%20%2B%202x%2C%20%E2%80%A6.&text=%E2%88%B4%20The%20total%20product%20in%20the%207%20years%20is%204375.

Answer 2

Answer:

• The production in the first year, ‘a’ is 550

• The total product in the 7 years is 4375.

• The product in the 10th year is 775.

Step by step explanation

Given: 600 and 700 radio sets units are produced in third and seventh year respectively.

a₃ = 600 and a₇ = 700

(i). The production in the first year We need to find the production in the first year.

Let first year production be ‘a’

So the AP formed is, a, a + x, a + 2x, ….

By using the formula,

aₙ = a + (n - 1)d

a₃ = a + (3 - 1)d

600 = a + 2d …. (i)

a₇ = a + (7 - 1)d

700 = a + 6d

a = 700 – 6d…. (ii)

Substitute value of a in (i) we get,

600 = a + 2d

600 = 700 – 6d + 2d

700 – 600 = 4d

100 = 4d

d = 100/4

= 25

Now substitute value of d in (ii) we get,

a = 700 – 6d

= 700 – 6(25)

= 700 – 150

= 550

∴ The production in the first year, ‘a’ is 550

(іі) the total product in the 7 years

We need to find the total product in 7 years i.e. is S₇

By using the formula,

Sₙ = n/2 [2a + (n - 1)d]

n = 7, a = 550, d = 25

S₇ = 7/2 [2(550) + (7 - 1)25]

= 7/2 [1100 + 150]

= 7/2 [1250]

= 7 [625]

= 4375

∴ The total product in the 7 years is 4375.

(ііі) the product in the 10ᵗʰ year.

We need to find the product in the 10ᵗʰ year i.e. a₁₀

By using the formula,

aₙ = a + (n-1)d

n = 10, a = 550, d = 25

a₁₀ = 550 + (10 - 1)25

= 550 + (9)25

= 550 + 225

= 775

∴ The product in the 10th year is 775.

Answer:-

• The production in the first year, ‘a’ is 550

• The total product in the 7 years is 4375.

• The product in the 10th year is 775.

I hope it's help you...Shreya♡♡♡☺