Answer :
a = 7n + 2
a₁ = 7*1 + 2 = 9
a₂ = 7*2 + 2 = 16
a₃ = 7*3 + 2 = 23
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a₂₀ = 7*20 + 2 = 142
This is an Arithmetic progression, a = 9, last term = 142
Sum of the 20 terms using: n/2(a + l) where l = last term.
= 20/2(9 + 142)
= 10 * 151
= 1510
Sum of the first 20 terms = 1510
a₁ = 7*1 + 2 = 9
a₂ = 7*2 + 2 = 16
a₃ = 7*3 + 2 = 23
.
.
.
a₂₀ = 7*20 + 2 = 142
This is an Arithmetic progression, a = 9, last term = 142
Sum of the 20 terms using: n/2(a + l) where l = last term.
= 20/2(9 + 142)
= 10 * 151
= 1510
Sum of the first 20 terms = 1510
The sum of the first 20 terms of the sequence a(n)=7n+2 is 1510
The given sequence is:
a(n) = 7n + 2
The first term is a(1)
a(1) = 7(1) + 2
a(1) = 7 + 2
a(1) = 9
The last term is a(20)
a(20) = 7(20) + 2
a(20) = 140 + 2
a(20) = 142
The sum of the first n terms is:
[tex]S_n = \frac{n}{2}[a(1)+a(n)][/tex]
For the sum of the first 20 terms:
a(1) = 9, n = 20
[tex]S_{20} = \frac{20}{2} [9+142]\\\\S_{20} = 10(151)\\\\S_{20} = 1510[/tex]
The sum of the first 20 terms of the sequence a(n)=7n+2 is 1510
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