Let a be the first term, d be the common difference, and n be the number of terms.
We can use the A.P formula, which is:
Tn = a + (n - 1)d
Where Tn is the nth term.
From the given information, we have:
1. T7 = a + 6d = 23
2. Tn = a + (n - 1)d = 43
3. T2n = a + (2n - 1)d = 91
Now, let's use equations 1 and 3 to create a new equation and connect them:
a + 6d = 23 (multiply by 2)
2a + 12d = 46
a + (2n - 1)d = 91
Now subtract one equation from the other
(2n - 1)d - 12d = 91 - 46
d(2n - 13) = 45
Now we want to find the values of n, which is a natural number:
For d = 1,
(2n - 13) = 45
2n - 13 = 45
2n = 58
n = 29
We found a natural number for n, so we don't need to test other values of d.
Now we can find the value of a:
a + (n - 1)d = 43
a + (29 - 1)d = 43
a + 28d = 43
a + 28(1) = 43
a = 15
Thus, the values for the A.P are: a = 15, d = 1, and n = 29.
Given that T7=23,Tn=43 and T2n=91.for an A.P.find a,d and n...help please
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