In an A.P,the first term is 2, and the sum of the 1st and 6th term is 161/2 what is the 4th term
Solve it
The answer is 9 1/2
1st term a = 2; 6th term = a + (16-1)d = 2 + 5d
2 + (2 + 5d) = 161/2; 4 + 5d = 161/2
5d = 12.5 ∴ = 2.5
the 4th term is 2 + (4-1)2.5= 91/2
To find the 4th term of an arithmetic progression (A.P.), we need to use the given information about the A.P.
Let's start by understanding the basics of an A.P. An A.P. is a sequence of numbers in which the difference between any two consecutive terms is constant. This constant difference is called the "common difference," denoted by 'd.'
In this case, the first term (a₁) is given as 2. So, a₁ = 2.
The sum of the 1st and 6th term is given as 161/2. It means that the sum of the first and sixth term of the A.P. is 161/2.
a₁ + a₆ = 161/2
We can use the formula for the nth term of an A.P. to solve the problem. The formula for the nth term (aₙ) of an A.P. is given by:
aₙ = a₁ + (n - 1) × d
Now let's solve the equation a₁ + a₆ = 161/2 to find the common difference (d).
Since we know that a₁ = 2, we can substitute the values in the equation:
2 + a₆ = 161/2
Next, let's find a₆. Using the formula for the nth term, we substitute n = 6:
a₆ = a₁ + (6 - 1) × d
a₆ = 2 + 5d
Substituting this back into the equation, we get:
2 + 2 + 5d = 161/2
4 + 5d = 161/2
To simplify the equation, we can multiply both sides by 2 to cancel out the denominator:
8 + 10d = 161
Now, let's isolate 'd' by moving the constant term to the other side:
10d = 161 - 8
10d = 153
Finally, divide both sides by 10 to solve for 'd':
d = 153/10
So, the common difference (d) is 15.3.
Now that we have the first term (a₁ = 2) and the common difference (d = 15.3), we can find the 4th term (a₄) using the formula:
a₄ = a₁ + (4 - 1) × d
a₄ = 2 + 3 × 15.3
a₄ = 2 + 45.9
a₄ = 47.9
Therefore, the 4th term of the given A.P. is 47.9.