Find the sum of the terms of the arithmetic progression whose first term, last term and common difference are 3, 101 and 7 respectively.a.750b.780c.720d.810
Question
Find the sum of the terms of the arithmetic progression whose first term, last term and common difference are 3, 101 and 7 respectively.
a. 750
b. 780
c. 720
d. 810
Solution
To find the sum of the terms of an arithmetic progression, we can use the formula:
Sum = n/2 * (a + l)
where: n = number of terms a = first term l = last term
First, we need to find the number of terms (n). We can use the formula:
n = ((l - a) / d) + 1
where: l = last term = 101 a = first term = 3 d = common difference = 7
Substituting the values, we get:
n = ((101 - 3) / 7) + 1 = 14 + 1 = 15
Now, we can find the sum:
Sum = 15/2 * (3 + 101) = 7.5 * 104 = 780
So, the sum of the terms of the arithmetic progression is 780 (Option b).
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