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Which term of the AP:3,15,27,39,..... will …

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

Posted by Lucifer?? Morningstar?? 5 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 5 years, 7 months ago

GIVEN
54th term
a + 53 d
132 more than a54
a + 53d + 132
Therefore, this is your an (last term)
AP 3 15 27 39,...
first term 'a' = 3
Common difference 'd' = 15 - 3 = 12
an = a + 53d + 132
FORMULA
an = a + (n - 1)d
a + 53d + 132 = a + (n - 1)d
Subsitute the values of a and d
3 + 53x12 + 132 = 3 + ( n - 1) x 12
3 + 53x12 + 132 - 3 = 12( n - 1)
636 + 132 = 12( n - 1)
768 = 12( n - 1)
768 / 12 = n - 1
64 = n - 1
64 + 1 = n
n = 65
Therefore, the required term is 65th.

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