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Arithmetic Progressions

Question
CBSEENMA10007952
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 If 5th term of an A .P. is zero. Prove that its 23rd term is three times its 11th term. 

Solution

Let a be the first term and d be the common difference of the A .P.
We have,
a5 = 0 ⇒ a + 4d = 0 ⇒ a = – 4d
Now, a23 = a + 22d = –4d + 22d = 18d
And 3 (a11) = 3(a + 10d)
= 3(– 4d + 10d)
= 3(6d) = 18d
Hence, a23 = 3 (a11) Proved.

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 taxi fare after each km when the fare is Rs. 15 for the first km and Rs. 8 for each additional km.

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, . . .

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