arithmetic progression

Can anyone have a solution about how to find common elements in two arithmetic progressions?? E.g. First seq is 2,17,32,47,.... Second seq is 67,147,227,... First common term is 227. So how to find these common terms in any given sequences?

#ArithmeticProgression(AP)

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Find the n'th term of both the Progressions and equate them as follows:

Let the NUMBER of term which is same is 'n' in the first sequence and 'N' in the second sequence. Therefore, since it is same in both the sequences,

                                            2 + (n-1)*15  =  67 + (N-1)*80
                                     = > 2 + 15n - 15  =  67 + 80N - 80
                                     =>  15n - 13 = 80N - 13
                                     =>  3n = 16N

Since, we need to find the first common term, so the values of n and N for which it is true is 16 and 3 respectively. Therefore, n = 16...Putting it in 2 + (n-1)*15, we get the common term as 227...Volaa!!!!

A Former Brilliant Member - 6 years, 12 months ago

Ohh....excellent....gr8... Further we can find whole sequence also....it will be also an ap...we can find common difference by taking lcm of the differences of the two sequences....it means here lcm(d1,d2)=lcm(15,80)=240....so the sequence will be 227,467,707,...and so on...i knew how to find difference but i didnt know how to find first term....thnx..

Milind Joshi - 6 years, 12 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$