To find the common difference in the arithmetic progression (A.P), we can use the formula:
Tn = a + (n-1)d
Where Tn is the nth term, a is the first term, n is the term number, and d is the common difference.
Given that the first term (a) is 7 and the 10th term is twice the second term:
T10 = 7 + (10-1)d = 7 + 9d
T10 = 2(T2) = 2(a + (2-1)d) = 2(a + d) = 2(7 + d) = 14 + 2d
Now, we can solve the equation:
7 + 9d = 14 + 2d
Subtracting 2d from both sides:
7 + 7d = 14
Subtracting 7 from both sides:
7d = 7
Dividing both sides by 7:
d = 1
Therefore, the common difference is 1.
To find the 19th term, we can substitute the values into the formula:
T19 = a + (19-1)d
T19 = 7 + (18)(1)
T19 = 7 + 18
T19 = 25
Therefore, the 19th term is 25.
To calculate the sum of the first 28 terms, we can use the sum formula for an A.P:
Sn = (n/2)(2a + (n-1)d)
Given that n = 28, a = 7, and d = 1, we can substitute these values into the formula:
S28 = (28/2)(2(7) + (28-1)(1))
S28 = 14(14 + 27)
S28 = 14(41)
S28 = 574
Therefore, the sum of the first 28 terms is 574.
the first yerm of an A.p is 7 and 10th term is twice the second term calculate the 19th term
B. The sum of the first 28th terms
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