Question

by what least number should the given number 8820 be divided to get a perfect square number and in each case find the number whose square is the new number​

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>>Arithmetic Progressions

>>Sum of an AP

>>The first and the last terms of an AP ar

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The first and the last terms of an AP are 5 and 45 respectively. If the sum of all its terms is 400, find the common difference and the number of terms.

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Solution

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Let n be the total number of terms and d be the common difference.

Given:

First term=a=5

Last term =l=45

Sum of all terms =S

n

=400

S

n

=n/2[a+l]

400=n/2[5+45]

n/2=400/50

n=16

There are 16 terms in the AP.

Therefore, 45 is the 16th term of the AP.

45=a+(16−1)d

45=5+15d

40=15d

15d=40

d=8/3

Common difference =d=8/3

Common difference is 8/3 and the number of terms are 16.