Find the sum of the series 5 + 7 + 9+ 10 + 13 + 13 + 17 + 16 +.........to 40 terms.

Solution not provided.
Ans. 1570
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Find four numbers in A .P. whose sum is 20 and the sum of whose squares is 180.

Solution not provided.
Ans. –1,3,7, 11
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The ratio of the sums of and ‘n’ terms of an A .P. is m2 : n2. Show that the ratio of the mth and nth terms is (2m – 1) : (2n – 1).

Let ‘a’ be the first term and ‘d’ be the common difference of the A .P.



Let ‘a’ be the first term and ‘d’ be the common difference of
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In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?
The cost of digging a well for the first metre is Rs. 150 and rises by Rs. 50 for each succeeding metre.

Cost of digging the well after 1 metre of digging of Rs. 150 = a4
Cost of digging the well after 2 metres of digging
= Rs. 150 + Rs. 50
= Rs. 200 = a2
Cost of digging the well after 3 metres of digging
= Rs. 150 + Rs. 50
= Rs. 2a = a3
Cost of digging the well after 4 metres of digging
= Rs. 200 + Rs. 50
= Rs. 250 = a4
and so on.
a2 – a4 = Rs. 200 – Rs. 150 = Rs. 50
a3 – a2 = Rs. 250 – Rs. 200 = Rs. 50
a4 – a3 = Rs. 350 – Rs. 250 = Rs. 50
i.e., ak +1 – ak is the same every time.
So this list of numbers forms an A .P. with the first term a Rs. 150 and the common difference d = Rs. 50.

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In which of the following situations, does the list of numbers involved make an arithmetic progression, and why?
The taxi fare after each km when the fare is Rs. 15 for the first km and Rs. 8 for each additional km.


Taxi fare for 1 km = Rs. 15 = aTaxi fare for 2 kms
= Rs. 15 + Rs. 8 = Rs. 23 = aTaxi fare for 3 kms
= 23 + Rs. 8 = Rs. 31 = aTaxi fare for 4 kms
= Rs. 31 + Rs. 8 = Rs. 39 = a4
and so on.
a– a1 = Rs. 23 – Rs. 15 = Rs. 8
a3 – a2 = Rs. 31 – Rs. 23 = Rs. 8
a4 – a3 = Rs. 39 – Rs. 31 = Rs. 8
i.e., ak + 1 – ak is the same every time.

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