The sum of sixth term of a.p is 72 and the second term is seven times fifth term find the first term,common difference and the sum of tenth term
S6=72
6a+15d=72 call as eq 1
T2=7(a+4d)
a+d=7a+28d
6a+27d=0 call as eq 2
Consider the eq 1&2 simultaneously
6a+15d=72 eq 1
6a+27d=0 eq 2
Subtract 1&2
We get
-12d=72
d=-6
evaluate d=-6 in eq 2
We get a=27
To find s10
=10/2(2*27+(10-1)-4)
=5(54-36)
=5(18)
=90
garbled English, but I think you want
6/2 (2a+5d) = 72
a+d = 7(a+64d)
solve that for a and d, and then evaluate
10/2 (2a+9d)
Velocity 20m/s find the components of the planes velocity if take off angles is
a) 45° .
B)60°
C) 70°
To find the first term, common difference, and the sum of the tenth term of an arithmetic progression (AP), we need to use the given information and some formulas.
Let's denote the first term of the AP as 'a' and the common difference as 'd'.
Given:
The sum of the sixth term of the AP is 72. We can use the formula for the sum of an arithmetic series to determine this:
Sum of n terms (Sn) = (n/2) * [2a + (n-1)d]
Substituting the known values, we have:
72 = (6/2) * [2a + (6-1)d]
72 = 3 * [2a + 5d]
24 = 2a + 5d --- Equation 1
The second term is seven times the fifth term:
a + d = 7(a + 4d)
a + d = 7a + 28d
6a - 27d = 0 --- Equation 2
Now, we have a system of two equations (Equation 1 and Equation 2) with two unknowns (a and d). We can solve this system to find the values of a and d.
Divide Equation 2 by 3:
2a - 9d = 0 -- Equation 3
Adding Equation 1 and Equation 3:
24 + (2a - 9d) = 0
2a - 9d = -24 -- Equation 4
Now we have two equations (Equation 4 and Equation 2) with two unknowns (a and d).
We can solve this system of equations:
Multiply Equation 4 by 3:
6a - 27d = -72
Using Equation 2:
6a - 27d = 0
Comparing the two equations:
-72 = 0
The above equation is not true, which means there is no solution to this system of equations. This indicates that the given information is inconsistent or contradictory.
Hence, it is not possible to determine the first term, common difference, or the sum of the tenth term with the given information.