The 7th term of an A.p is 20 and the 13th term is 38 find the ,1,70thterm ,2,11thterm
a+6d = 20
a+12d = 38
so,
a=2
d=3
Can't make out which other terms you want, but knowing a and d should make it easy.
To find the 1st and 70th terms, we need to first identify the common difference (d) of the arithmetic progression (A.P).
The formula to find the nth term of an A.P is given by:
An = A + (n - 1)d
From the given information:
A7 = 20 and A13 = 38
Using the formula, we can set up two equations:
A7 = A + 6d = 20 ---(Equation 1)
A13 = A + 12d = 38 ---(Equation 2)
Now, we can solve these equations to find the values of A and d.
Subtract Equation 1 from Equation 2 to eliminate A:
(A + 12d) - (A + 6d) = 38 - 20
6d = 18
d = 3
Substituting the value of d back into Equation 1 to find A:
A + 6(3) = 20
A + 18 = 20
A = 20 - 18
A = 2
So, the first term (A1) is 2 and the common difference (d) is 3.
To find the 1st term, substitute n = 1 into the formula:
A1 = A + (1 - 1)d
A1 = A = 2
Therefore, the 1st term is 2.
To find the 70th term, substitute n = 70 into the formula:
A70 = A + (70 - 1)d
A70 = 2 + 69 * 3
A70 = 2 + 207
A70 = 209
Therefore, the 70th term is 209.
Now, let's move on to the 11th term.
To find the 11th term (A11), substitute n = 11 into the formula:
A11 = A + (11 - 1)d
A11 = 2 + 10 * 3
A11 = 2 + 30
A11 = 32
Therefore, the 11th term is 32.