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Arithmetic Progressions

Question

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How many terms of the AP 3, 5, 7,........must be taken so that the sum is 120 ?
(a) 9 (b) 10 (c) 11 (d) 12

Solution

straight S subscript straight n equals straight n over 2 left square bracket 2 straight a plus left parenthesis straight n minus 1 right parenthesis straight d right square bracket rightwards double arrow 120 equals straight n over 2 left square bracket 2 cross times 3 plus left parenthesis straight n minus 1 right parenthesis 2 right square bracket rightwards double arrow straight n equals 10

ans. (b)

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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