Question

Find the general term of the sequencec.1 { 10, 5, 0, -5, -10 }c.2 { 1, 4, 9, 16, 25 }​

Answer 1

Answer:

1. 15 - 5n where n>=1

2. n² where n>=1

Step-by-step explanation:

1. {10, 5, 0, -5, -10} is an Arithmetic Progression

nth term is a + (n - 1)d

where a = first term, n= nth term, d= common difference.

a = 10, d = -5 (5-10, 0-5, -5-0, -10-(-5))

Therefore, nth(General) term of the sequence:

= 10 + (n - 1)-5

= 10 + (-5n) + 5

= 10 + 5 - 5n

= 15 - 5n

Test:

if n = 1; 15 - 5(1) = 10

if n = 2; 15 - 5(2) = 5

if n = 3; 15 - 5(3) = 0 and so on.

2. {1, 4, 9, 16, 25}

The general term of the sequence is n²

Test:

if n = 1; 1² = 1

if n = 2; 2² = 4

if n = 3; 3² = 9 and so on.