First term (52) plus (number of terms minus 1) multiplied by common difference (12) equals the 102nd term, which is 1264. Option D is the right choice.
Recognize the formula for an arithmetic series term:
The nth term of an arithmetic series (A) can be found using the formula:
An = A1 + (n - 1)d
where:
An is the nth term
A1 is the first term
n is the term number
d is the common difference
Plug in the given values:
We are given A1 = 52, n = 102, and d = 12:
A102 = 52 + (102 - 1) * 12
A102 = 52 + 101 * 12
A102 = 52 + 1212
A102 = 1264
The 102nd term of the arithmetic series is 1264.
Option D is the right choice.
Question:-
Find the 102nd term, given the first term and the common difference. A1 = 52 and d = 12.
a) 1240
b) 1252
c) 1264
d) 1276