The 16th of an A.P is 93 given that it's common different is 6 find the first 28th
a28 - a16 = 12d
so,
a28 - 93 = 12*6
To find the first term of the arithmetic progression (AP) with a common difference of 6 and a 16th term of 93, we can use the formula for the nth term of an AP:
An = A1 + (n - 1) * d
where An is the nth term, A1 is the first term, n is the number of the term in the AP, and d is the common difference.
Given that the 16th term (An) is 93, we can substitute the values into the formula to find A1:
93 = A1 + (16 - 1) * 6
Simplifying:
93 = A1 + 15 * 6
93 = A1 + 90
Subtracting 90 from both sides:
93 - 90 = A1
3 = A1
Therefore, the first term (A1) of the AP is 3.
To find the 28th term of the AP, we can again use the formula:
A28 = A1 + (28 - 1) * d
Substituting the values:
A28 = 3 + (28 - 1) * 6
Simplifying:
A28 = 3 + 27 * 6
A28 = 3 + 162
A28 = 165
So, the 28th term of the AP is 165.
To find the first term of an Arithmetic Progression (A.P.), we can use the formula:
First term (a) = Nth term (An) - (n - 1) * Common difference (d)
In this case, we are given the 16th term (An = 93), the common difference (d = 6), and we want to find the 28th term. So, we can rearrange the formula to solve for the first term:
a = An - (n - 1) * d
Substituting the given values:
a = 93 - (28 - 1) * 6
Simplifying:
a = 93 - 27 * 6
a = 93 - 162
a = -69
Therefore, the first term of the A.P. is -69.