If the nth term of A. P. are 7, 12, 17, 22is equal to the nth term of another A. P. 27, 30, 33, 36. Find the value of n?​

Step-by-step explanation:

We are given two arithmetic sequences:

7, 12, 17, 22... and 27, 30, 33, 36...

And we want to determine n such that the nth term of each sequence is equivalent.

We can write a direct formula for each sequence. Recall that the direct formula for an arithmetic sequence is given by:

Where a is the initial term and d is the common difference.

The first sequence has an initial term of 7 and a common difference of 5. Hence:

The second sequence has an initial term of 27 and a common difference of 3. Hence:

Set the two equations equal to each other:

Solve for n. Distribute:

Combine like terms:

Isolate:

Divide. Hence:

In conclusion, the 11th term of the first A.P. is equivalent to the 11th term of the second.

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step-by-step explanation: