The partial sum 1+4+7+⋯+79 equals

Question

The partial sum 1+4+7+⋯+79 equals

Answer 1

1 + 4 + 7 + ... + 79 is an arithmetic sequence with a common difference of 3. 4-1 =3, 7-4=3,

a1 = 1, d= 3

an = a1 + d(n-1)

an = 1 + 3(n-1) =1 +3n-3 = 3n-2 = 79

3n = 81

n = 81/3 = 27

the 27th term is 79

26th term is 76

sn = (n/2)(a1+an)

s27= (27/2)(1+a27)

s27 = (27/2)(1+79) = 27(40)= 1080

sum of the 1st 27 terms = 1080

s2 = (2/2)(1+4) = 5

s3 = (3/2)(1+7) = 12

s4 = (4/2)(1+10) = 22

s5 = (5/2)(1+13) =35

...

s26 = (26/2)(1+76) = (13)(77) = 1001

s27 = (27/2)(1+79) = 27(40)=1080