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Arithmetic Progressions
Question
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If 9th term of an A .P. is zero. Prove that 29th term is double of its 19th term. 

Answer

 Let a be the first term and d be the common difference of the A .P. we have,
a9 = 0 ⇒ a + 8d = 0 ⇒ a = – 8d
Now, a29 = a + 28d = –8d + 28d = 20d
2(a19) = 2(a + 18d) = 2(– 8d + 18d)
= 2(10d) = 20d
Hence, a29 = 2 (a19)

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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 = – 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, . . .

Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.
 –10, –6, –2, 2, ....