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Arithmetic Progressions

Question
CBSEENMA10008074
Wired Faculty App

Find the sum of the series :
34 + 32 + 30 +........ + 10

Solution
Let ‘a’ be the firs term and ‘d’ the common difference, then
a = 34,    d = - 2, an = 10 = l
We know that,  an = a + (n - 1) d
rightwards double arrow   10 = 34 + (n - 1) (- 2)
rightwards double arrow   10 = 34 - 2n + 2
rightwards double arrow   10 = 36 - 2n
rightwards double arrow   - 26 = - 2n
rightwards double arrow      n = 13
And,   S subscript n equals n over 2 left square bracket a space plus space l k right square bracket S o comma space S subscript 13 equals 13 over 2 left square bracket 34 plus 10 right square bracket equals 13 over 2 cross times 44 equals 13 cross times 22 equals 286

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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