Question

The algebraic expression of the sum to n terms of an arithmetic sequence is 4n2+5n
Find the first term amd common difference. Write the algebraic expression of the arithmetic sequence

Answer 1

EXPLANATION.

• GIVEN

algebraic expression of the sum to n terms of

an Ap = 4n² + 5n

To find.

1) = First term.

2) = common difference.

3) = write algebraic expression of Ap.

According to the question,

Tn terms of an Ap = Tn = Sn - S(n - 1)

replace the value of n to ( n - 1 )

=> 4n² + 5n - [ 4 ( n - 1 )² + 5 ( n - 1 ) ]

=> 4n² + 5n - [ 4 ( n² + 1 - 2n ) + 5n - 5 ]

=> 4n² + 5n - [ 4n² + 4 - 8n + 5n - 5 ]

=> 4n² + 5n - 4n² - 4 + 8n - 5n + 5

=> 8n + 1

Put the value of n in equation

we get,

=> put n = 1 = 8 + 1 = 9

=> put n = 2 = 8(2) + 1 = 17

=> put n = 3 = 8(3) + 1 = 25

=> put n = 4 = 8(4) + 1 = 33

Therefore,

sequence will be written as

=> 9,17,25,33.......

First term = a = 9

common difference = d = b - a = 17 - 9 = 8

Therefore,

1) = First term = 9

2) = common difference = 8

3) = algebraic expression = 8n + 1