The 10th term of an a.p is -27 and the 5th term is -12 what is the 18th term? Find also the sum of its 25 term
pls I need the answer complete
"10th term of an a.p is -27---> a + 9d = -27
" 5th term is -12" ----> a + 4d = -12
subtract them , the a's drop out and you can find d
then find a
then use your formulas for term(18) and sum(25)
Good
Pls I need the answer complete
To find the 10th term of an arithmetic progression (a.p.), we need to know the first term (a) and the common difference (d). However, in this case, we are not given these values directly.
We are given the 5th term (t5) and the 10th term (t10). Let's use this information to find the common difference (d) and the first term (a) using the formula for the nth term of an a.p.
The formula for the nth term of an a.p. is:
tn = a + (n-1)d
For the 5th term, we have:
t5 = a + (5-1)d (1)
For the 10th term, we have:
t10 = a + (10-1)d (2)
Given t5 = -12 and t10 = -27, we can substitute these values into equations (1) and (2) to get two equations.
From equation (1):
-12 = a + 4d (3)
From equation (2):
-27 = a + 9d (4)
Now, we have two equations (3) and (4) with two variables (a and d). We can solve these equations simultaneously to find the values of a and d.
Subtracting equation (3) from equation (4) eliminates variable a:
-27 - (-12) = a + 9d - (a + 4d)
-27 + 12 = 9d - 4d
-15 = 5d
d = -15/5
d = -3
Now that we have found the common difference (d), we can substitute it back into equation (3) to find the first term (a).
-12 = a + 4(-3)
-12 = a - 12
a = 0
Therefore, the first term (a) is 0 and the common difference (d) is -3.
To find the 18th term (t18), we can use the formula for the nth term of an a.p. as follows:
t18 = a + (18-1)d
= 0 + 17(-3)
= -51
Therefore, the 18th term is -51.
To find the sum of the first 25 terms (S25) of the a.p., we can use the formula for the sum of an arithmetic series:
Sn = (n/2)(2a + (n-1)d)
Substituting the values, we have:
S25 = (25/2)(2(0) + (25-1)(-3))
= (25/2)(-50)
= -625
Therefore, the sum of the first 25 terms is -625.