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