To find the first term and the sum of its 100 terms, we can use the formulas for the nth term and the sum of an arithmetic progression.
Let's assume the first term of the AP is "a" and the common difference is "d".
From the given information, we can write two equations:
a + 9d = 68 (equation 1, as the 10th term is 68)
a + 3d = 26 (equation 2, as the 4th term is 26)
We can solve these two equations simultaneously to find the values of "a" and "d".
Subtracting equation 2 from equation 1, we get:
(a + 9d) - (a + 3d) = 68 - 26
6d = 42
d = 42/6
d = 7
Now substitute the value of d in equation 2:
a + 3(7) = 26
a + 21 = 26
a = 26 - 21
a = 5
Therefore, the first term of the AP is 5.
To find the sum of its 100 terms, we can use the formula:
Sum = (n/2)(2a + (n-1)d)
Here, n = 100, "a" = 5, and "d" = 7.
Sum = (100/2)(2(5) + (100-1)(7))
Sum = 50(10 + 99(7))
Sum = 50(10 + 693)
Sum = 50(703)
Sum = 35150
Therefore, the sum of the 100 terms of the AP is 35150.
In an A.p ,the 1oth is 68 and the 4th term is 26 .find the first term and the sum of its 100 term
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