Consider the arithmetic sequence where the 12th term is 41 and the 4th term is 1. a. Find the formula of the nthterm of the sequence. b. Find the sum of the first 20 terms.
Mathematics · High School · Thu Jan 21 2021
Answered on
Given :
a12 = 41
Or a + 11d = 41 …1
a4 = 1
Or, a + 3d = 1 …2
Using elimination method:
Subtracting equation 2 from 1, we get
a + 11d - a - 3d = 41 - 1
8d = 40
d = 40/8
d = 5
Now, putting value of d in equation 2, we get
a + 3(5) = 1
a = 1 - 15
a = - 14
(a). nth term of sequence :
an = a + (n-1)d
an = -14 + (n -1)5
= -14 + 5n - 5
= -19 + 5n
(b). Sum of first 20 terms :
Sn = n/2[2a + (n-1)d]
= 20/2[2×(-14) + (20-1)5]
= 10[-28 + 19 × 5]
= 10[-28 + 95]
= 10[67]
= 670
So, sum of first 20 terms is 670.