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Arithmetic Progressions

Question
CBSEENMA10007558
Wired Faculty App

How many three-digit numbers are divisible by 7?

Solution
Three-digit numbers divisible by 7 are:
105, 112, 119,  ...., 994.
Here,         a = 105
                 d = 112 - 105 = 7
and            an = 994
We know that,
                an = a + (n -1)d
rightwards double arrow   994 = 105 + (n - 1) x 7
rightwards double arrow   994 - 105 = 7 x (n - 1)
rightwards double arrow   889 = 7 x (n - 1)
rightwards double arrow space space space space space space space straight n minus 1 space space space equals space 889 over 7 equals 127 rightwards double arrow space space space space space space space space space space straight n space equals space 127 space plus space 1 space equals space 128
Hence, 128 three digit numbers are divisible by 7.

Some More Questions From Arithmetic Progressions Chapter

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

For the following APs, write the first term and the common difference
3, 1, – 1, – 3, . . .

For the following APs, write the first term and the common difference
– 5, – 1, 3, 7, . . .

For the following APs, write the first term and the common difference
0.6, 1.7, 2.8, 3.9, . . .

Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.
– 1.2, – 3.2, – 5.2, – 7.2, . . .

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