Question -
Answer -
Given:
600 and 700 radio setsunits are produced in third and seventh year respectively.
a3 =600 and a7 = 700
(і) The production in thefirst year
We need to find theproduction in the first year.
Let first yearproduction 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 ain (i) we get,
600 = a + 2d
600 = 700 – 6d + 2d
700 – 600 = 4d
100 = 4d
d = 100/4
= 25
Now substitute valueof d in (ii) we get,
a = 700 – 6d
= 700 – 6(25)
= 700 – 150
= 550
∴ The production in thefirst year, ‘a’ is 550
(іі) the total product inthe 7 years
We need to find thetotal 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 inthe 7 years is 4375.
(ііі) the product in the 10th year.
We need to find theproduct 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 yearis 775.