Respuesta :
Number of terms = 48
common difference = 1.5
This question involves the concept of Arithmetic Progression.
- The formula for sum of an arithmetic progression series with first and last term given is;
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex](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; [tex]S_{n}[/tex] = 1920
- Plugging in relevant values into the sum of an AP formula, we have;
1920 = [tex]\frac{n}{2}[/tex](4 + 76)
simplifying this gives;
1920 = 40n
n = 1920/40
n = 48
- Formula for nth term of an AP is;
[tex]t_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1)d
where;
[tex]a_{1}[/tex] is first term
d is common difference
n is number of term
[tex]t_{n}[/tex] 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
