Question

plz can anyone tell why this step is done
the question is
a man arranges to pay off debt of 3600 by 40 installment which forms an AP when 30 installments paid he dies leaving one third of debt unpaid,find the value of first installment

Answer 1

Hey

Here is your answer

Let the first installments be a
Given that the installments are in AP.
Let the common difference be d
Hence the installments are: a, a + d, a + 2d ………..40th term
Recall the nth term of AP, tn = a + (n – 1)d
⇒ t40 = a + (40 – 1)d = a + 39d
Sn = n/2 ( a+l )
Sum of n term of AP,
S40 = 40/2 ( a + a + 39d )
Given total debt = Rs 3600
⇒ 20[2a + 39d] = 3600
2a + 39d = 180 → (1)
It is also given that 30 installments are paid.
Unpaid amount = one-third of Rs 3600 = Rs 1200
Therefore total payment till 30 installments = 3600 – 1200
= Rs 2400
Now, sum of 30 terms,
S30 = 30/2 ( a+a+29d )
= 15(2a + 29d)
⇒ 15(2a+29d) = 2400
2a +29d = 160 → (2)
Subtract (2) and (1), we get
2a + 39d = 180
2a +29d = 160
--------------------
10d = 20
∴ d = 2
Put d = 2 in equation (1)
2a + 29(2) = 180
⇒ 2a + 58 = 180
⇒ 2a = 180 – 58 = 122
∴ a = 61
8th installment, t8 = a + 7d
= 61 + 7(2)
= 61 + 14 = 75

Hope it helps you!