Calculate s58 for the arithmetic sequence {an}= {5/6n+1/3} if you could show me the steps that would be great. i keep following the directions in the lesson and getting 8,613/6 but all i have to choose from for answers are 146/3 91/2 8671/6 9267/6

Answer is 8671/6 which is the third choice

Work Shown:

Find the first term of the sequence by plugging in n = 1

a_n = (5/6)*n + 1/3

a_1 = (5/6)*1 + 1/3    replace n with 1

a_1 = 5/6 + 1/3

a_1 = 5/6 + 2/6

a_1 = 7/6

Repeat for n = 58 to get the 58th term

a_n = (5/6)*n + 1/3

a_58 = (5/6)*58 + 1/3    replace n with 58

a_58 = (5/6)*(58/1) + 1/3

a_58 = (5*58)/(6*1) + 1/3

a_58 = 290/6 + 1/3

a_58 = 145/3 + 1/3

a_58 = 146/3

Now we can use the s_n formula below with n = 58

s_n = (n/2)*(a_1 + a_n)

s_58 = (58/2)*(a_1 + a_58)    replace n with 58

s_58 = (58/2)*(7/6 + a_58)   replace a_1 with 7/6

s_58 = (58/2)*(7/6 + 146/3)   replace a_58 with 146/3

s_58 = (58/2)*(7/6 + 292/6)

s_58 = (58/2)*(299/6)

s_58 = (58*299)/(2*6)

s_58 = 17342/12

s_58 = 8671/6

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!

b

step-by-step explanation:

u take $75 minus $60.the anwer/original($75)multiply by 100