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Arithmetic Progressions
Question
Wired Faculty App

Find the sum of the :
First 25 terms of an A .P. whose nth term is given by an= 7 – 3n. z

Answer

Sn = 5n2 + 3n
⇒ Sn – 1 = 5(n – 1)2 + 3(n – 1)
∴ Sn – Sn – 1 = (5n2 + 3n) – [5(n – 1)2 + 3(n – 1)}
⇒ an = (5n2 + 3n) – {5 (n2 – 2n + 1) + 3n – 3}
= (5n2 + 3n) – {5n2 – 10n + 5 + 3n –3}
= 5n2 + 3n – 5n2 + 7n – 2
= 10n – 2
Hence, required nth term is 10n – 2

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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 = –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, . . .

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