1.The 43rd term of an A.p is 26 find the first term of the progression given that its common difference is ½
To find the first term of an arithmetic progression (A.P), we can use the formula:
an = a1 + (n - 1)d
where:
an = nth term
a1 = first term
n = term number
d = common difference
Given that the 43rd term (an) is 26 and the common difference (d) is 1/2, we can substitute these values into the formula:
26 = a1 + (43 - 1)(1/2)
Simplifying the equation:
26 = a1 + 42/2
26 = a1 + 21
Subtracting 21 from both sides:
26 - 21 = a1
5 = a1
Therefore, the first term (a1) of the arithmetic progression is 5.
To find the first term of an arithmetic progression (A.P.) given the 43rd term and the common difference, we can use the formula:
a + (n - 1)d = T
where:
a = first term of the A.P.
n = term number
d = common difference
T = nth term of the A.P.
In this case, we know the 43rd term is 26, and the common difference is 1/2. Let's substitute these values into the formula to find the first term (a).
a + (43 - 1)(1/2) = 26
Simplifying the equation:
a + 42/2 = 26
a + 21 = 26
a = 26 - 21
a = 5
Therefore, the first term of the arithmetic progression is 5.