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Arithmetic Progressions

Question
CBSEENMA10009635
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Find the 60th term of the AP 8, 10,12, ..., if it has a total of 60 terms and hence find the sum of its last 10 terms.

Solution

The given AP is 8, 10, 12, ....
So,
First term =a = 8
Common difference = d = 10-8 =2
We know that nth term of an AP, an = a + (n - 1)
60th term of the given AP = a60 = 8 +( 60-1) x  2 = 8 + 59 x 2 = 8 + 118 = 126
Therefore, the 60th term of the given AP is 126
It is given that the AP has a total of 60 terms. So, in order to find sum of last n terms. we take
First term, A = 126
Common difference, D = -2
Now,
Sum space of space straight n space term space of space AP space from space the space end space equals space straight n over 2 left square bracket 2 straight A space plus left parenthesis straight n space minus space 1 right parenthesis space straight D right square bracket therefore space Sum space of space last space 10 space terms space of space the space given space AP equals space 10 over 2 left square bracket space 2 space straight x space 126 space plus space left parenthesis 10 space minus space 1 space right parenthesis space straight x space left parenthesis negative 2 right parenthesis right square bracket equals space 5 space left square bracket 252 space plus 9 space straight x space left parenthesis negative 2 right parenthesis right square bracket equals space 2 space left parenthesis 252 space minus 18 right parenthesis equals space 5 space straight x space 234 equals space 1170 hence space comma space the space sum space of space last space 10 space terms space of space the space given space AP space is space 1170

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 – 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, . . .

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

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