The first term and last term of an arithmetic progression are -4 and 145 respectively. If the common difference is 4. (a) find the 12th term (b) find the 25th term.
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To find the nth term of an arithmetic progression, you can use the formula:
nth term = first term + (n - 1) * common difference
Given that the first term (a1) is -4 and the common difference (d) is 4, we can find the 12th term (a12) and 25th term (a25) using this formula.
(a) To find the 12th term (a12):
a12 = -4 + (12 - 1) * 4
= -4 + 11 * 4
= -4 + 44
= 40
Therefore, the 12th term of the arithmetic progression is 40.
(b) Similarly, to find the 25th term (a25):
a25 = -4 + (25 - 1) * 4
= -4 + 24 * 4
= -4 + 96
= 92
Therefore, the 25th term of the arithmetic progression is 92.
To find the nth term (where n is a positive integer) of an arithmetic progression, use the formula:
nth term = first term + (n - 1) * common difference
For this problem, we are given that the first term (a₁) is -4, the last term (aₙ) is 145, and the common difference (d) is 4.
(a) To find the 12th term, substitute n = 12 into the formula:
12th term = -4 + (12 - 1) * 4
Simplify:
12th term = -4 + 11 * 4
Calculate:
12th term = -4 + 44
12th term = 40
Therefore, the 12th term of the arithmetic progression is 40.
(b) To find the 25th term, substitute n = 25 into the formula:
25th term = -4 + (25 - 1) * 4
Simplify:
25th term = -4 + 24 * 4
Calculate:
25th term = -4 + 96
25th term = 92
Therefore, the 25th term of the arithmetic progression is 92.