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

The sum of the first $n$ terms of an arithmetic progression (A.P.) is given by $S_n = 2n^2 + 3n$ . What is the $5^{\text{th}}$ term of the progression?

$21$ Answer
B
$65$
C
$44$
D
$25$

Answer

The

5^{\text{th}}

term of the arithmetic progression is

21

The

n^{\text{th}}

term of a sequence can be determined from its sum formula using

T_n = S_n - S_{n-1}

. Evaluating

S_5 = 2(5)^2 + 3(5) = 65

and

S_4 = 2(4)^2 + 3(4) = 44

, the difference

T_5 = 65 - 44 = 21

gives the correct value of the

5^{\text{th}}

term.

Step-by-Step Solution

Calculate the sum of the first 5 terms (

S_5

)

S_5 = 2(5)^2 + 3(5) = 2(25) + 15 = 65

To find the sum up to the

5^{\text{th}}

term using the given formula

S_n = 2n^2 + 3n

Calculate the sum of the first 4 terms (

S_4

)

S_4 = 2(4)^2 + 3(4) = 2(16) + 12 = 44

To find the cumulative total of all terms prior to the

5^{\text{th}}

term.

Subtract

S_4

from

S_5

to isolate the

5^{\text{th}}

term (

T_5

)

T_5 = S_5 - S_4 = 65 - 44 = 21

The

n^{\text{th}}

term of any sequence is given by the relation

T_n = S_n - S_{n-1}

Key Concept

Relationship between the sum of

n

terms (

S_n

) and the

n^{\text{th}}

term (

T_n

) in an Arithmetic Progression

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

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