Question

Solve the given question.​

Answer 1

ANSWER:

Given:

• Letters written in each set by each person = 4
• Cost of mailing one letter = 50paise

To Find:

• Amount spent on postage when 8th set of letter is mailed.

Solution:

We are given that,

⇒ Letters posted in 1st set = 4

⇒ Letters posted in 2nd set = 4 × 4 = 16

⇒ Letters posted in 3rd set = 16 × 4 = 64

So, according to the above information, a sequence is formed.

Sequence being:

⇒ 4, 16, 64, . . .

As we can see,

⇒ 16/ 4 = 64/16 = 4

So, the given sequence becomes a GP.

In this GP,

⇒ a = first term = 4, r = common ratio = 4

To find the amount spend on postage when 8th set of letter is mailed, we need to find the number of letters posted in the 8th set.

So, total number of letters posted in 8th set.

We know that, sum of n terms of GP is,

⇒ Sₙ = a(rⁿ - 1)/(r - 1)

Hence,

⇒ S₈ = 4(4⁸ - 1)/(4 - 1)

We know that,

⇒ 4⁸ = 65536

⇒ S₈ = 4(65536 - 1)/3

⇒ S₈ = 4(65535)/3

⇒ S₈ = 4 × 21845

⇒ S₈ = 87380

We have that,

⇒ Cost of mailing one letter = 50paise

So,

⇒ Cost of mailing 87380 letters = (87380 × 50)paise

⇒ Cost of mailing 87380 letters = ₹ (87380 × ¹/₂)

⇒ Cost of mailing 87380 letters = ₹ 43690

Hence, Amount spent on postage when 8th set of letters is mailed is ₹ 43690