Find the 4th term from the end of the AP -11, -8, -5, .........., 49.
Common difference = d = a2 - a1 = -8 - (-11) = 3
If 49 is the nth term,
a(n) = a1 + (n-1)d
=> 49 = -11 + (n-1)3
=> 60 = 3n - 3
=> n = 21
So, 4th term from the end is the 18th term
a(18) = a1 + (18-1)d
= -11 + 17(3)
= -11 + 51
= 40
To find the 4th term from the end of the arithmetic progression (AP) -11, -8, -5, .........., 49, we need to identify the first and second terms of the AP, as well as the common difference.
In an arithmetic progression, each term is obtained by adding a constant value, called the common difference, to the previous term. For instance, in the given AP, we have:
First term (a₁) = -11
Common difference (d) = -8 - (-11) = 3
Since the terms are given in decreasing order, we can re-arrange the AP in ascending order with their corresponding position:
n → 1 2 3 4 5 6 7 ......... 61
Term → 49 46 43 40 37 34 31 ......... -11
To find the fourth term from the end, we consider the fourth term from the beginning, which is the 61st term. Therefore, n = 61.
To find the corresponding term, we can use the formula for the nth term of an arithmetic progression:
aₙ = a₁ + (n-1)d
Substituting the given values into the formula:
a₆₁ = -11 + (61 - 1) × 3
Simplifying:
a₆₁ = -11 + 60 × 3
a₆₁ = -11 + 180
a₆₁ = 169
Therefore, the 4th term from the end of the AP -11, -8, -5, .........., 49 is 169.
once you know d=3, just subtract it 3 times from 49:
49-3*3 = 40