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Arithmetic Progressions

Question
CBSEENMA10009788
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For what value of n, are the nth terms of two A.Ps.  63, 65, 67,…. and 3, 10, 17,….. equal?

Solution

For A.P.  63, 65, 67,........, we have

First term = 63  and common difference = 65-63 = 2

Hence, nth term = an = 63 + (n-1) 2

⇒an = 63 + 2n - 2 = 2n + 61

 

For A.P.  3, 10, 17,........, we have 

First term = 3 and  common difference = 10-3 = 7

Hence,  ntn term = an = 3 + (n-1) 7

⇒an = 3 + 7n - 7 = 7n - 4The two A.Ps. will have identical nth term, if an = an ⇒2n + 61 = 7n - 4⇒5n = 65⇒n = 13

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 = 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, . . .

Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.
– 1.2, – 3.2, – 5.2, – 7.2, . . .

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