The third term of a linear sequence is 20 and the sum of the first ten terms is 275. Find: (A) The first term and the common difference. (B). The 37th term of the progression.

Answer 1

a+2d = 20
10/2 (2a+9d) = 275
Now just solve for a and d, and then find a+36d

Answer 2

Oobleck I don't understand how I will solve a and d still confusinf

Answer 3

If you're studying AP's, you must have had Algebra I. Next step: rearrange the equations a bit.
a + 2d = 20
10a + 45d = 275
Now solve by substitution or elimination, and you will have the values for a and d.

Answer 4

How did you get the common difference

Answer 5

45

Answer 6

a+2d= 20(×10) equation 1
10a+45d=275.(×1) Equation 2
10a-10a=0
2d-45d= 200-275
-25d/25=-75/25
d=3
Substitute in equation 1 when d is 3
a+2(3)=20
a+6=20
a=14
1b. a+36d
= 14+108
=122

Answer 7

20d -45d not 2d