an = 3 n + 7
n = 1
a1 = 3 ∙ 1 + 7 = 3 + 7 = 10
n = 2
a2 = 3 ∙ 2 + 7 = 6 + 7 = 13
13 - 10 = 3
n = 3
a3 = 3 ∙ 3 + 7 = 9 + 7 = 16
16 - 13 = 3
etc.
This is AP where first term is a1 = 10 and common difference d = 3
In AP:
an = a1 + ( n - 1 ) d
a20 = a1 + 19 d
a20 = 10 + 19 ∙ 3 = 10 + 57
a20 = 67
Sum on n term in AP:
Sn = n ( a1 + an ) / 2
In this case n = 20:
S20 = 20 ( a1 + a20 ) / 2
S20 = 20 ( 10 + 67 ) / 2 = 20 ∙ 77 / 2 = 770
If n term of an AP is (3n+7), then find the sum of first 20 terms.
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