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Arithmetic Progressions

Question
CBSEENMA10007527

Which term of the AP : 3, 8, 13, 18, . . . ,is 78?

Solution

The given A. P. is 3, 8, 13, 18, .....
Here,     a = 3
             d = 8 - 3 = 5
Let the nth term f=of the A. P. be 78
Then,   a= a + (n - 1)d
space space rightwards double arrow space space space  78 = 3 + (n -1) (5)
 rightwards double arrow     5(n - 1) = 78 - 3
 rightwards double arrow     5 (n - 1) = 75
 rightwards double arrow space space space space space space n minus 1 equals 75 over 5
       
 rightwards double arrow     n - 1 = 15
 rightwards double arrow     n = 15 + 1
 rightwards double arrow     n = 16
Hence, 16th term of the A .P. is 78.