the fifth term of an arithmetic progression is 40 and the seventh term is 28 more than the 3rd term. Find the first and 10th term.

Step-by-step explanation:

t5 = a + (5-1)d

t5 = a + 4d

40 = a + 4d

t3 = a + 2*d

t7 = a + 2d + 28 = a + 6d

Start with the seventh term which has 2 equal answers

a + 2d + 28 = a + 6d                    Subtract a from both sides

2d + 28 = 6d                                Subtract 2d from both sides

28 = 4d                                         Divide by 4

28/4 = d

d  = 7

t5 = a + 4d = 40

a + 4*7 = 40

a = 40 - 28

a = 12

First term is 12

10th term is

t10 = 12 + (10 - 1)*7

t10 = 12 + 9*7

t10 = 75

Interesting question. Thanks for posting

paula, cory, and krista