Question

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For what value of n, the nth term of the following two A.P.’s are equal?​

Answer 1

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→ 1st AP

63,65,67........

→ WE KNOW THAT ,

a^n = a + ( n - 1 ) d

HENCE ,

a = 63

d = 65 - 63 = 2

→ Putting these in formula

a^n = a + ( n - 1 ) d

= 63 + ( n - 1 ) × 2

= 63 + 2n - 2

= 61 + 2n

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→ 2nd AP

3,10,17......

→ We know that ,

a^n = a + ( n - 1 ) d

Hence ,

a = 3

d = 10 - 7 = 3

→ Putting these in formula ,

a^n = a + ( n - 1 ) d

= 3 + ( n - 1 ) 7

= 3 + 7n - 7

= 7n - 4

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→ Given that ,

nth term of 1st AP = nth term of || AP

61 + 2n = 7n - 4

61 + 4 = 7n - 2n

65 = 5n

65 / 5 = n

= 13

n = 13

Answer 2

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