Justify whether it is true to say that the following are the nth terms of an AP.
(i) 2n–3 (ii) 3n2+5 (iii) 1+ n + n2
In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers.
(i) The fee charged from a student every month by a school for the whole ses- sion, when the monthly fee is Rs 400.
(ii) The fee charged every month by a school from Classes I to XII, when the monthly fee for Class I is Rs 250, and it increases by Rs 50 for the next higher class.
(iii) The amount of money in the account of Varun at the end of every year when Rs 1000 is deposited at simple interest of 10% per annum.
(iv) The number of bacteria in a certain food item after each second, when they double in every second.
The taxi fare after each km, when the fare is Rs 15 for the first km and Rs 8 for each additional km, does not form an AP as the total fare (in Rs) after each km is
15, 8, 8, 8, …
Is the statement true? Give reasons.
Two APs have the same common difference. The first term of one AP is 2 and that of the other is 7. The difference between their 10th terms is the same as the difference between their 21st terms, which is the same as the difference between any two corresponding terms. Why?
For the AP: –3, –7, –11, …, can we find directly a30 – a20 without actually finding a30 and a20? Give reasons for your answer.
Which of the following form an AP? Justify your answer.
(i) –1, –1, –1, –1, …
(ii) 0, 2, 0, 2, …
(iii) 1, 1, 2, 2, 3, 3,…
(iv) 11, 22, 33,…
(v) 1/2, 1/3, 1/4…..
(vi) 2, 22, 23, 24, …
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