Question

you are intending to make savings weekly that will follow an arithmetic sequence. If on the 4th week you were able to save Php120 and on the 6th week you saved Php150 What to do: - Design 2 equations in terms of A1 and d to present your savings pattern - show how you use your two equations to help you find the savings on the 1st week - show how you will find the savings on the 10th week - can you do the saving plan? why or why not

Answer 1

Given :- you are intending to make savings weekly that will follow an arithmetic sequence. If on the 4th week you were able to save Php120 and on the 6th week you saved Php150.

To find :- show how you use your two equations to help you find the savings on the 1st week - show how you will find the savings on the 10th week ?

Solution :-

Given,

→ On 4th week i was able to solve = php120 .

→ On 6th week i was able to solve = php150 .

and,

→ savings follows an arithmetic sequence.

we know that,

• nth term of an AP is given by :- a + (n - 1)d, where a is first term of AP and d is common difference .

Let first week of my saving is a and each week it is increasing by d.

So,

→ 4th term of AP = a + (4 - 1)d = a + 3d .

→ 6th term of AP = a + (6 - 1)d = a + 5d .

Therefore,

→ a + 3d = php120 ----------- Eqn.(1)

→ a + 5d = php150 ----------- Eqn.(2)

Subtracting Eqn.(1) from Eqn.(2) we get,

→ (a + 5d) - (a + 3d) = php150 - php120

→ a - a + 5d - 3d = php30

→ 2d = php30

dividing both sides by 2,

→ d = php15.

Putting value of d in Eqn.(1) ,

→ a + 3(php15) = php120

→ a + 45php = php120

→ a = php120 - 45php

→ a = php75 .

Hence,

→ my saving on 10th week = a + (10 - 1)d = a + 9d = php75 + 9*php15 = php75 + php135 = php210 (Ans.)

∴ my saving on first week is php75 and my saving on 10th week is php210.