Solution:

Here, a = 23,d = 25−23 = 2

and 2 nd AP = −17,−10, −3,4,...

Here, a = -17, d = −10 − ( −17) = −10 + 17 = 7

According to the question,

23 + (n−1)2 = −17 + (n−1)7

23 + 2n−2 = −17+7n−7

21 + 2n = −24 + 7n

2n − 7n = 24 − 21

−5n = −45

n = 9

• 9th term of the given AP's are same

• Now, we will find the 9th term

We have,

[tex]a_{n} \: = \: a + (n - 1)d[/tex]

[tex]a _{9} = 23 + (9 - 1)2[/tex]

[tex]a _{9} = \: 23 + 8 \times 2[/tex]

[tex]a _{9} = 23 + 16[/tex]

[tex]a _{9} = 39[/tex]

Explanation:

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