Question

SUM OF THE FIRST 4 TERMS OF AN ARITHMETIC SEQUENCE IS 72. SUM OF FIRST 9 TERMS IS ALSO 72. a) WHAT IS THE FIFTH AND SEVENTH TERM OF THE SEQUENCE AND WHAT IS THE COMMON DIFFERENCE.​

Answer 1

Answer:

Let the terms of the A.P. be a, a+d, a+2d, …..

Sum of first 4 terms = 72

Or, (4/2) * [ 2a + (4–1) d ] = 72

Or, 2 (2a + 3d) = 72

Or, 2a + 3d = 36 (Equation 1)

Sum of first 9 terms = 72

Or, 9/2 * [ 2a + (9–1) d ] = 72

Or, 2a + 8d = 72 * 2/9

Or, 2a + 8d = 16 (Equation 2)

Subtracting Equation 1 from Equation 2, we get, 5d = —20

Or, d = —4

Substituting the value of 'd' in Equation 1, we get, 2a — 12 = 36

Or, 2a = 48

Or, a = 24

Therefore, the terms of the A.P. are

24, 24 + (—4), 24 + 2(—4), …….

i.e., 24, 20, 16,…..

5th term = 8

7th term = 0

Common difference (d) = -4