Question

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

Answer 1

Step-by-step explanation:

refer the attachment hope it helps

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Answer 2

Question:-

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

Solution:-

Let's find ${n}^{th}$ term of both APs

1st AP

63,65,67,...

We know that formula is

${a}_n$ = a + (n - 1)d

Here,

a = 63

d = 65 - 63 = 2

By putting these with formula

${a}_n$ = a + (n - 1)d

= 63 + (n - 1) × 2

= 63 + 2n - 2

= 61 + 2n

2nd AP

3,10,17,...

As we know that formula is

${a}_n$ = a + (n - 1)d

Here,

a = 3

d = 10 - 3 = 7

By putting these with formula

${a}_n$ = a + (n - 1)d

= 3 + (n - 1)7

= 3 + 7n - 7

= 7n - 4

Given that

${n}^{th}$ term of 1st AP = ${n}^{th}$ term of 2nd AP

61 + 2n = 7n - 4

61 + 4 = 7n - 2n

65 - 5n

$\frac{65}{5}$ = n

13 = n

n = 13