Respuesta :
Answer:
94.5
Step-by-step explanation:
sₙ = n/2 * (2a₁ + (n-1)d) ... Sₙ: sum of first n term d: common difference
sum of the first 20 terms: 20/2 * (2a₁ + (20-1)d) = 10* (2a₁+19d) = 405
2a₁+19d = 40.5 ... (1)
sum of the first 40 terms: 40/2 * (2a₁ + (40-1)d) = 20* (2a₁+39d) =1410
2a₁+39d = 70.5 ... (2)
(2)-(1): 20d = 30
d = 1.5
a₁ = 1/2 (40.5 - 19*1.5) = 6
aₙ = a₁ + (n-1)d
60th term: a₆₀ = 6 + (60-1)*1.5 = 94.5
The 60th term of the given progression is 94.5
What is the general form of arithmetic progression?
[tex]a_n = a_1+ (n-1)d[/tex]
[tex]s_n = n/2 * (2a_1 + (n-1)d) ... S_n[/tex]sum of first n term
d: common difference
We have to find sum of the first 20 terms therefore use n=20
[tex]20/2 * (2a_1 + (20-1)d) = 10* (2a_1+19d) = 405[/tex]
[tex]2a_1+19d = 40.5[/tex] ... (1)
sum of the first 40 terms:
[tex]40/2 * (2a_1 + (40-1)d) = 20* (2a_1+39d) =1410[/tex]
[tex]2a_1+39d = 70.5[/tex] ... (2)
(2)-(1):
20 d = 30
divide both side by 20 and isolate d
d = 1.5
[tex]a_1= 1/2 (40.5 - 19\times1.5) = 6[/tex]
[tex]a_n = a_1+ (n-1)d[/tex]
for the 60th term use n=60
[tex]a_{60}= 6 + (60-1)\times1.5 = 94.5[/tex]
Therefore we get the 60th term of the given progression is 94.5
To learn more about the arithmetic progression visit:
https://brainly.com/question/18828482
