CBSE Class 10-Mathematics: Chapter –5 Arithmetic Progressions Part 18
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Question 3:
A sum of Rs is to be used to give seven cash prizes to students of a school for their overall academic performance. If, each prize is Rs less than its preceding term, find the value of each of the prizes.
Answer:
It is given that sum of seven cash prizes is equal to .
And each prize is R.s 20 less than its preceding term.
Let value of first prize Rs. a
Let value of second prize
Let value of third prize
So, we have sequence of the form:
It is an arithmetic progression because the difference between consecutive terms is constant.
First term , Common difference
Applying formula, to find sum of n terms of AP, we get
Therefore, value of first prize
Value of second prize
Value of third prize
Value of fourth prize
Value of fifth prize
Value of sixth prize
Value of seventh prize
Question 4:
A spiral is made up of successive semicircles, with centers alternatively at A and B, starting with center at A, of radii , , , , … What is the total length of such a spiral made up of thirteen consecutive semicircle?

A Spiral is Made up of Successive Semicircles
Answer:
Length of semi-circle
Length of semicircle of radii
Length of semicircle of radii
Length of semicircle of radii
Therefore, we have sequence of the form:
terms .
To find total length of the spiral, we need to find sum of the sequence terms
Total length of spiral terms
Total length of spiral terms … (1)
Sequence terms is an arithmetic progression.
Let us find the sum of this sequence.
First term , Common difference and
Applying formula, to find sum of n terms of AP, we get
Therefore, terms
Putting this in equation (1), we get
Total length of spiral