(b)find the first five terms of the exponential sequence and the sum of the first n terms
(a) The first five terms of the linear sequence are 2, 5, 10, 17, and 26. The sum of the first n terms is given by Sn = n(n+1)/2.
(b) The first five terms of the exponential sequence are 2, 8, 32, 128, and 512. The sum of the first n terms is given by Sn = 2^n - 1.
the first and second term of an exponential sequence are respectively the first and third term of a linear sequence the fourth term of the linear sequence is 10 and the sum of it's first five terms is 60 (a)find the first five terms of a linear sequence and the sum of the first n terms
2 answers
The terms in the bot's answers don't even satisfy the given conditions !!!
first information: term1 of the AS = term1 of the GS, so a = a
term2 of the GS = ar, term2 of the AS = a+d, so a+d = ar, (let that sit)
2nd information:
"the fourth term of the linear sequence is 10 " ...... a + 3d = 10 **
"the sum of it's first five terms is 60" ... (5/2)(2a + 4d) = 60
2a + 4d = 24
a + 2d = 12 ***
subtract *** from ** to get d = -2, which gives us a = 16
back in a+d = ar
16-2 = 16r ...... r = 7/8
our AS is : 16, 14, 12, 10, 8, ...
sum(n) = (n/2(32 + (n-1)(-2))
= (n/2)(34 - 2n) = n(17 - n)
our GS is :16, 14, 49/4, 343/32, ....
All conditions are met,
my answer is correct, the bot is wrong!
first information: term1 of the AS = term1 of the GS, so a = a
term2 of the GS = ar, term2 of the AS = a+d, so a+d = ar, (let that sit)
2nd information:
"the fourth term of the linear sequence is 10 " ...... a + 3d = 10 **
"the sum of it's first five terms is 60" ... (5/2)(2a + 4d) = 60
2a + 4d = 24
a + 2d = 12 ***
subtract *** from ** to get d = -2, which gives us a = 16
back in a+d = ar
16-2 = 16r ...... r = 7/8
our AS is : 16, 14, 12, 10, 8, ...
sum(n) = (n/2(32 + (n-1)(-2))
= (n/2)(34 - 2n) = n(17 - n)
our GS is :16, 14, 49/4, 343/32, ....
All conditions are met,
my answer is correct, the bot is wrong!