The sum of the arithmetic progression 4, ..., 76 is 1920. Find the number of terms and the common difference.
1 answer:
<u>Number of terms = 48 </u>
<u>common difference = 1.5 </u>
This question involves the concept of Arithmetic Progression.
The formula for sum of an arithmetic progression series with first and last term given is; = (a + l)
where;
a = first term
l = last term
n = number of terms
From the given sequence, we see that; first term; a = 4
last term; l = 76
Sum of A.P; = 1920
Plugging in relevant values into the sum of an AP formula , we have; 1920 = (4 + 76)
simplifying this gives;
1920 = 40n
n = 1920/40
n = 48
Formula for nth term of an AP is; = + (n - 1)d
where;
is first term
d is common difference
n is number of term
is the nth term in question
the 48th term is 76
Thus;
76 = 4 + (48 - 1)d
76 - 4 = 47d
72 = 47d
d = 72/47
d ≈ 1.5
Thus;
Number of terms = 48
common difference = 1.5
Read more at; brainly.com/question/16935540
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