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Arithmetic Progressions

Question
CBSEENMA10007556

Which term of the AP : 3, 15, 27, 39, . . . will be 132 more than its 54th term?

Solution

Given A.P. is : 3, 15,27,39.....
Here a1 = 3, a2 = 15
a3 = 27, a4 = 39
d = a2 – a1 = 15 – 3 = 12
a54 = a (54 – 1)d
= 3 + 53 x 12
= 3 + 636 = 639
Let ntn term be 132 more than a54 We know that,
a= a + (n - 1)d
a54 + 132 =  a + (n - 1)d
rightwards double arrow 639 + 132 = 3 + (n - 1) x 12
rightwards double arrow 771 - 3 = 12(n - 1)
rightwards double arrow space 768 = 12(n - 1)
rightwards double arrow space straight n minus 1 equals 768 over 12 equals 64
rightwards double arrow space straight n space equals space 64 space plus space 1 space equals space 65