Question

For what value of n’. are the nth terms of two APs: 63, 65, 67, ……. and 3, 10, 17, ……….. equal?​

Answer 1

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To Solve:

• value of n where 2 APs are equal.

Given:

• 1ˢᵗ - 63, 65, 67, …

• 2ⁿᵈ - 3, 10, 17, …

Solⁿ:

• Form Eqⁿ from both the APs and put them equal.

1st AP =>

a¹ = 63

d = 2ㅤㅤㅤ(a² - a¹ = 65-63 = 2)

aⁿ = ?

n = ?

1st AP Eqⁿ =>

aⁿ = a+ ( n-1 ) d

aⁿ = 63 + ( n-1 ) 2

aⁿ = 63 + 2n - 2

aⁿ = 61 + 2n --------(1)

______________________

2nd AP =>

a¹ = 3

d = 7

aⁿ = ?

n = ?

2nd AP Eqⁿ =>

aⁿ = a+ ( n-1 ) d

aⁿ = 3+ ( n-1 ) 7

aⁿ = 3+ 7n - 7

aⁿ = -4 + 7n -------(2)

_______________________

ATQ ;

$61 + 2n = 7n - 4 \\ \\ 61 + 4 = 7n - 2n \\ \\ 65 = 5n \\ \\ \frac{{ \cancel{65}}}{{ \cancel{5}}} = n \\ \\ { \boxed{ \color{teal}{13 = n}}}$

» So, At 13th Term the AP will Equal.

HOPE IT HELPS

MARK BRAINLIEST PLS :)