The 18th term of an A.p is 25.(a) find it's first term when the common difference is 2.(b) what term of an A.p gives 49
T18=a+17d=25
T18=a+(18-1)d
T18=a+17d=25
a+(17×2)=25
a+34=25
a=25-34
a=-9
Pls solve this questions
To find the first term of an arithmetic progression (A.P), we need to use the formula:
nth term (Tn) = a + (n-1)d
where Tn is the nth term of the A.P, a is the first term, n is the position of the term, and d is the common difference.
(a) Given that the 18th term (T18) is 25 and the common difference (d) is 2, we can substitute these values into the formula to find the first term (a).
T18 = a + (18-1)*2
25 = a + 34
25 - 34 = a
a = -9
Therefore, the first term (a) when the common difference is 2 is -9.
(b) To find the term that gives 49, we set Tn = 49 and solve for n in the formula mentioned above.
49 = a + (n-1)d
49 = a + (n-1)*2
Since we are given the common difference (d) as 2, we can substitute this value into the equation:
49 = a + (n-1)*2
49 = a + 2n - 2
Now, substitute the value of the first term (a) that you obtained in part (a) (-9):
49 = -9 + 2n - 2
49 + 9 + 2 = 2n
58 = 2n
n = 29
Therefore, the 29th term of the A.P will give 49.
its, not it's in this context.
a+17d = 25
since d=2, it is simple to get a.
Then, since 49-25=24, and 24/2 = 12, the 18+12=30th term is 49.
Solve it mathematically
(a) Well, if the 18th term of the arithmetic progression is 25, and the common difference is 2, we can use the formula for the general term of an arithmetic progression, which is given by a + (n-1)d, where a is the first term, n is the term number, and d is the common difference.
So, for the 18th term, we have:
25 = a + (18-1)*2
25 = a + 17*2
25 = a + 34
To solve for a, let's isolate a:
a = 25 - 34
a = -9
So, the first term of the arithmetic progression when the common difference is 2 is -9.
(b) To find which term of the arithmetic progression gives 49, we can use the same formula. Let's call this term number "n":
49 = a + (n-1)*d
Since we don't know the first term (a) or the common difference (d), we can't solve for n. I guess I'm no comedian when it comes to this question. Let me give you a joke instead: Why don't scientists trust atoms? Because they make up everything!