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mestny [16]
3 years ago
10

The sum of the first 30 terms of the sequence an=6n+5 is

Mathematics
2 answers:
Bingel [31]3 years ago
8 0

Answer:

S_{30}=2940.

Step-by-step explanation:

Given  : a_{n} =6n+5.

To find : The sum of the first 30 terms .

Solution: We have given a_{n} =6n+5.

For n = 1

a_{1} =6(1)+5.

a_{1} =6+5.

a_{1} =11.

For n =2

a_{2} =6(2)+5.

a_{2} =17.

Common difference = 17 - 11 = 6.

Sum of nth term : S_{n} =\frac{n}{2}[2a+(n-1)d].

d = common difference = 6.

For  n = 30 .

S_{30} =\frac{30}{2}[2(11+(30-1)6].

S_{30} =15[22+29 *6].

S_{30} =15[22+29 *6].

S_{30} =15[22+174].

S_{30} =15[196].

S_{30}=2940.

Therefore, S_{30}=2940.

ra1l [238]3 years ago
3 0
First term a1 = 6+5 = 11
second term = 12+5 = 17

common difference = 6  

Sum of n terms:-
Sn  = (n/2) [ 2a1 + d(n - 1)]
Sum of 30 terms:-
S30  = (30/2)[ 2*11 + 6(30-1)]
        =  15 * ( 22 + 174)
        =   15 * 196
         =   2940 Answer

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