THE 4th and 7th term of a.p are 15 and 27 respectively.find (a)the 1st term (b) common difference
a + 3 d = 15
a + 6 d = 27
----------------- subtract
-3 d = - 12
d = 4
onward and upward
In an Arithmetic Progression:
an = a1 + ( n - 1 ) d
where
a1 = the initial term
d = the common difference of successive members is d,
an = the nth term
In this case:
a4 = a1 + ( 4 - 1 ) d = 15
a1 + 3 d = 15
a7 = a1 + ( 7 - 1 ) d = 27
a1 + 6 d = 27
Now you must solve system:
a1 + 3 d = 15
a1 + 6 d = 27
___________
Try to solve it.
The solution is a1 = 3 , d = 4
Yours A.P.
3 , 7 , 11 , 15 ,19 , 23 , 27...
The 4th and 7th term of a.p are 15 and 27 respectively. Find (a) the 1st term (b) common difference
Ah, I just told you how to do it.
To find the 1st term and the common difference of an arithmetic progression (AP) given the 4th and 7th terms, you can use the following steps:
Step 1: Identify the formula for the nth term of an AP.
In an AP, the nth term (Tn) can be calculated using the formula:
Tn = a + (n - 1) * d
Where:
- Tn represents the nth term of the AP
- a is the 1st term of the AP
- n is the position of the term in the AP
- d is the common difference of the AP
Step 2: Set up the equations using the given information.
From the problem, we know that:
- The 4th term (T4) is 15
- The 7th term (T7) is 27
Using the formula from Step 1 and substituting the positions and values, we get the following:
T4 = a + (4 - 1) * d = 15
T7 = a + (7 - 1) * d = 27
Step 3: Solve the equations simultaneously.
We have two equations with two unknowns (a and d), so we can solve them simultaneously to find the values.
From the first equation, rearrange it to solve for a:
a + 3d = 15 ----(1)
From the second equation, rearrange it to solve for a:
a + 6d = 27 ----(2)
Step 4: Solve the simultaneous equations.
To solve the equations (1) and (2), we can use the method of substitution or elimination. Here, let's use the elimination method.
Subtract equation (1) from equation (2) to eliminate a:
(a + 6d) - (a + 3d) = 27 - 15
3d = 12
d = 4
Now, substitute the value of d (4) back into equation (1), and solve for a:
a + 3(4) = 15
a + 12 = 15
a = 15 - 12
a = 3
Step 5: Interpret the results.
(a) The 1st term (a) is 3.
(b) The common difference (d) is 4.
Therefore, the 1st term is 3 and the common difference is 4 for the given arithmetic progression (AP).