Answer:
n = 13
Step-by-step explanation:
AP = 2, 10, 17 ...
AP1 = 63,65, 67
Find the general term of AP
L = a + (n - 1)*d
a = 2
d = 7
Find the general term of AP1
L = 63 + (n - 1)*d
a = 63
d = 2
Equation to equate both of them
L = 3 + (n-1)7
L1 = 63 + (n - 1)*2
Equate L and L1
2 + (n - 1)*7= 63 + (n-1)*2 Subtract 3 from both sides
(n - 1)*7 = 63 - 3 + (n - 1)*2 Remove the brackets
7n - 7 = 60 + 2n - 2 Combine the like terms on the right
7n - 7 = 58 + 2n Subtract 2n from both sides
7n - 2n -7 = 58 Add 7 to both sides
5n = 58 +7 Divide by 5
n = 65/5
n = 13
So the 13th term on each series is equal.
L_13 = 3 + (13 - 1)*7
L_13 = 3 + (12)*7
L_13 = 87
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L'_13 = 63 + (13 -1 ) * 2
L'_13 = 63 + 12*2
L'_13 = 87
