For an arithmetic sequence where a1 = 13 and the common difference is 3, find s7.

a. 157
b. 151
c. 154
d. 162
10 points show steps

D ) 154

Step-by-step explanation:

a 1 = 13,  d = 3;

S n = n/2 * ( a 1 + a n )

a 7 = a 1 + 6 d = 13 + 3 * 6 = 13 + 18 = 31

S 7 = 7/2 * ( 13 + 31 ) = 7/2 * 44 = 154

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places