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Arithmetic Progressions

Question
CBSEENMA10007533
Wired Faculty App

Find the number of terms in each of the following APs :
7, 13, 19, . . . , 205

Solution

7, 13, 19, . . . , 205
Here,      a = 7
              d = 13 - 7 = 6
And,        an = 205
Let the number of terms be n.
Then,    an = 205
rightwards double arrow  a + ( n - 1) d = 205
rightwards double arrow  7 + ( n - 1)6 = 205
rightwards double arrow  6(n - 1) = 205 - 7
rightwards double arrow  6(n - 1) = 198
rightwards double arrow space space space space space n minus 1 equals 198 over 6
rightwards double arrow    n - 1 = 33
rightwards double arrow    n = 33 + 1
rightwards double arrow    n = 34
Hence, the number of terms of the given A .P., is 34.

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.

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

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, . . .

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