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Arithmetic Progressions
Question
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How many numbers of two digits are divisible by 7?

Answer

Two digits numbers, which are divisible by
7 are, 14, 21, 28.......... 98.
Here, a = 14, d = 7 and l = 98
We know that, Tn = a + (n –1)d
⇒ 98 = 14 + (n – 1) (7)
[∵ l = Tn]
⇒ 98 = 14 + 7n – 7
⇒ 98 = 7n + 7
⇒ 98 = 7 = 7n
⇒ 91 = 7n ⇒ n = 13
Hence, number of terms (n) = 13.

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Some More Questions From Arithmetic Progressions Chapter

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.

In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?

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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.

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a – 10, d = 10

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a = –2, d = 0

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a = 4, d = – 3

Write first four terms of the AP, when the first term a and the common difference d are given as follows:

a = – 1.25, d = – 0.25