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Arithmetic Progressions

Question
CBSEENMA10007854
Wired Faculty App

In an A.P. 
Given a = 8, an = 62, Sn = 210, find ‘n’ and ‘d’.



Solution

Here a = 8
straight a subscript straight n space equals space 62 end subscript
Sn = 210
We know that, an = a + (n - 1)d
rightwards double arrow   62 - 8 = (n - 1)d
rightwards double arrow   54 = (n -d)d                   ...(i)
And,  Sn = n over 2 '[ 2a - (n - 1) d
rightwards double arrow  210 = n over 2[ 2 x 8 + (n - 1) d]
rightwards double arrow  420 = n[16 +(n - 1)d] .......(ii)
From (i) and (ii), we get
420  = n[ 16 + 54]
rightwards double arrow   420  = 70n
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Putting this value of n in (i) we get
54 = (6 -1) x d
rightwards double arrow     5d = 54
rightwards double arrow     d = 54 over 5
Hence,  n = 6 and d = space space 54 over 5.

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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