Question

What is the sum of the first 30 terms of this arithmetic sequence? 6,13,20,27,34

Answer 1

Answer:

3135

Step-by-step explanation:

Givens

a1 = 6

Use t4 - t3 to get d

t4 = 27

t3 = 20

Step One

Find a1 and d

a1 = 6

d = t4 - t3

d = 27 - 20

d = 7

Step Two

Find the 30th Term

tn= a1 + (n -1 )*d

t30 = 6 + (30 - 1) * 7

t30 = 6 + 29*7

t30 = 6 + 203

t30 = 209

Step Three

Find the sum using Sum = (a + t30)*n/2

n = 30              given

a1 = 6               given  

t30 = 209         calculated from step 2

Sum = (a1 + t30)*n/2        Substitute

Sum = (6+ 209)*30/2       Combine like terms and divide by 2

sum = 215 * 15                  Multiply

Sum = 3135                      Answer