The first term and last term of an arithmetic progression are -3 and 145 respectively .if the common difference is 4.(a) find the 12th term (b) find the 25th term.
You are told a=-3 and d = 4
so you can find any term using:
term(n) = a + (n-1)d
so term(12) = a + 11d = -3 + 11(4) = ....
find term(25) in the same way.
(the fact that the last term is 145 is not needed.
I will add the question , What term number is 145 ?
I think to solve this, you will be getting an equation -3+(x-1)4, solve for x and it will be your answer
Oh, arithmetic progressions, always counting on you for some mathematical fun! Let's get started!
(a) To find the 12th term, we can use the formula for the nth term of an arithmetic progression: an = a1 + (n-1)d. Here, a1 is the first term (-3), d is the common difference (4), and n is the term we want to find (12).
So, the 12th term can be calculated as follows:
a12 = a1 + (12-1)d
= -3 + (11)(4)
= -3 + 44
= 41!
(b) Now, for the 25th term, we'll use the same formula, but this time n is 25. Let's see what we get:
a25 = a1 + (25-1)d
= -3 + (24)(4)
= -3 + 96
= 93!
There you have it! The 12th term is 41 and the 25th term is 93. Always glad to bring some comedy to the world of numbers!
To find the nth term of an arithmetic progression, we can use the formula:
nth term = first term + (n - 1) * common difference
Given:
First term (a) = -3
Last term (l) = 145
Common difference (d) = 4
To find the 12th term:
(a) Find the 12th term:
Using the formula, we have:
12th term = a + (12 - 1) * d
Substituting the values:
12th term = -3 + (12 - 1) * 4
12th term = -3 + 11 * 4
12th term = -3 + 44
12th term = 41
Therefore, the 12th term of the arithmetic progression is 41.
(b) Find the 25th term:
Using the formula, we have:
25th term = a + (25 - 1) * d
Substituting the values:
25th term = -3 + (25 - 1) * 4
25th term = -3 + 24 * 4
25th term = -3 + 96
25th term = 93
Therefore, the 25th term of the arithmetic progression is 93.