Question

a quadratic equation has firth termsof 80 and tenth term of 315 and has second constant difference of 6 find the general term​

Answer 1

Answer:

Constant Differences

In the first part of this unit we consider sequences where the difference between

successive terms is the same every time. We also use formulae to create the terms

of a sequence.

Example 1

Write down the next 3 terms of each of the following sequences:

(a) 7, 11, 15, 19, 23, ...

(b) 1, 9, 17, 25, 33, ...

Solution

(a) 7 11 15 19 23 ...

4444

The difference between each term and the next is always 4. This value is

called the first difference. So we can continue the sequence by adding 4

each time. This gives the sequence:

7, 11, 15, 19, 23, 27, 31, 35

(b) 1 9 17 25 33 ...

8888

Here the difference between each term and the next is always 8. To

continue the sequence we must keep on adding 8 every time. This gives

the sequence:

1, 9, 17, 25, 33, 41, 49, 57

Example 2

A sequence is defined by the formula u n n = + 3 1.

Calculate the first 5 terms of this sequence.

Solution

The first term, often called u 1 , is formed by substituting n = 1 into the formula.

u 1 = 311 × +

= 3 1 +

= 4