The sum of the first n terms of an arithmetic progression (AP) is given by S_n = 2n^2 + 3n… — JAMB UTME

The sum of the first $n$ terms of an arithmetic progression (AP) is given by $S_n = 2n^2 + 3n$ . What is the $8^{\text{th}}$ term of the progression?

Cevap: 33

The

8^{\text{th}}

term of the arithmetic progression is

33

The

n^{\text{th}}

term of any sequence can be calculated using the identity

T_n = S_n - S_{n-1}

. Substituting

n = 8

gives

S_8 = 2(8)^2 + 3(8) = 152

, and substituting

n = 7

gives

S_7 = 2(7)^2 + 3(7) = 119

. Therefore,

T_8 = 152 - 119 = 33

Calculate the sum of the first 8 terms (

S_8

) by substituting

n = 8

into

S_n = 2n^2 + 3n

S_8 = 2(8)^2 + 3(8) = 128 + 24 = 152

The sum formula provides the total sum of terms from

T_1

T_8

Calculate the sum of the first 7 terms (

S_7

) by substituting

n = 7

into

S_n = 2n^2 + 3n

S_7 = 2(7)^2 + 3(7) = 98 + 21 = 119

The sum formula provides the total sum of terms from

T_1

T_7

Subtract

S_7

from

S_8

to determine the value of the

8^{\text{th}}

term (

T_8

T_8 = S_8 - S_7 = 152 - 119 = 33

The difference between the sum of the first

n

terms and the sum of the first

(n-1)

terms yields the

n^{\text{th}}

term (

T_n = S_n - S_{n-1}

Finding the nth term of a sequence from the sum of the first n terms using

T_n = S_n - S_{n-1}

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