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Arithmetic Progressions
Question
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The sum of the 4th and 8th terms of an A .P. is 24 and the sum of the sixth and tenth terms is 44. Find the First three terms of the A .P.

Answer

It is given that,
a4 + a8 = 24
⇒ a + 3d + a + 7d = 24
⇒ 2 a+ 10d = 24
⇒ a + 5d = 24 (i)
And,
a6 + a10 = 44
⇒ a + 5d + a + 9d = 44
⇒ 2a + 14d = 44
⇒ a + 7d = 22 (ii)
solving (i) and (ii) we get
a = –13 and d = 5
Hence, the first three terms are
a, a + d, a + 2d
⇒ – 13, (–13 + 5), (–13 + 2 x5)
= –13, –8,–3
⇒ 2a + 14d = 44
Problems Based on sum of ‘n’ th term of an A .P

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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.

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, . . .