The 7th term of an A.p is 20 and the 13th term is 38 find the ,1,70thterm ,2,11thterm
Pagalo, use ur mind dont ask with other.
To find the 1,70th term and 11th term of the arithmetic progression (A.P.), we need to use the formula for the nth term of an A.P.
The formula for the nth term of an A.P. is:
nth term = a + (n - 1)d
Where:
a = first term of the A.P.
n = position of the term
d = common difference between consecutive terms of the A.P.
Let's first find the common difference (d) of the A.P. using the given information.
Given:
7th term (a7) = 20
13th term (a13) = 38
Step 1: Find the common difference (d):
a7 = a + 6d
20 = a + 6d
a13 = a + 12d
38 = a + 12d
Step 2: Solve the simultaneous equations to find a and d.
Subtracting the equations, we get:
38 - 20 = a + 12d - (a + 6d)
18 = 6d
d = 3
Substituting the value of d in either equation, we can find a:
20 = a + 6(3)
20 = a + 18
a = 2
Now that we have the values of a (first term) and d (common difference), we can find the 1,70th term and the 11th term.
1. To find the 1,70th term:
nth term = a + (n - 1)d
n = 70
1,70th term = 2 + (70 - 1)3
1,70th term = 2 + 69 * 3
1,70th term = 2 + 207
1,70th term = 209
Therefore, the 1,70th term of the A.P. is 209.
2. To find the 11th term:
nth term = a + (n - 1)d
n = 11
11th term = 2 + (11 - 1)3
11th term = 2 + 10 * 3
11th term = 2 + 30
11th term = 32
Therefore, the 11th term of the A.P. is 32.