Answer:
341
STEPS:
an = a1 + (n-1) d
a1 is the first number
d = is the difference between each number = 6
a11 = 1 + (11 - 1)6
a11 = 61
Sn = n (a1 + an)/2
S11 = 11 (1 + 61)/ 2
S11 = 682/2
S11 = 341 = answer
The 11th partial sum of the arithmetic sequence {1, 7, 13, 19, …} = 341
An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k.
[tex]a_{n} = a_{1} + (n-1)d\\\\[/tex]
Given : {1, 7, 13, 19.....}
[tex]a_{1} = 1\\\\d = a_{2} - a_{1} = 7 - 1 = 6\\\\a_{n} = 1 + 6(n-1) = 1 + 6n - 6 = 6n -5\\\\a_{11} = 6*11 -5 = 61\\\\S_{n} = \frac{n(a_{1} + a_{n})}{2} \\\\S_{11} = \frac{11(1+ 61)}{2} = 11 * 31 = 341[/tex]
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