Question

1) if for an a.p., tn=2n+2 then t5=? a) 20 b) 15 c) 12 d) 18​

Answer 1

Question:-

If for an AP ; tₙ = 2n + 2 ; then t₅ = ?

Answer:-

Given:-

tₙ = 2n + 2

Substitute n = 5 to find the 5th term.

⟹ t₅ = 2(5) + 2

⟹ t₅ = 10 + 2

⟹ t₅ = 12

∴ The 5th term of the given AP is 12 (Option - C).

Additional Information:-

• A series in which each term (except first term) differs from its preceding term by a fixed quantity is called an Arithmetic Progression (AP).

• The fixed quantity is called common difference.

• General form of an AP is a , a + d .... if a is the first term and d is the common difference.

• nth term of an AP is a + (n - 1)d.

• Sum of n terms of an AP (Sₙ) = n/2 [ 2a + (n - 1)d ] or n/2(a + l) [ Here, a is the first term and l is the last term ]

Answer 2

Answer:

Given :-

• An A.P is tn = 2n + 2.

To Find :-

• What is the value of t₅.

Solution :-

Given :

• n = 5

Then, according to the question,

↦ $\sf t_n = 2n + 2$

↦ $\sf t_5 =\: 2(5) + 2$

↦ $\sf t_5 =\: 2 \times 5 + 2$

↦ $\sf t_5 =\: 10 + 2$

➠ $\sf\bold{\red{t_5 =\: 12}}$

$\therefore$ The value of t₅ is 12.

Hence, correct options is option no (c) 12.

IMPORTANT FORMULA :-

$\longmapsto$ $\sf a_n =\: a + (n - 1)d$

where,

• $\sf a_n$ = nth term of the sequence.
• a = First term of sequence.
• d = Common difference.

$\longmapsto$ $\sf S_n =\: \dfrac{n}{2}\bigg[2a + (n - 1)d\bigg]$

where,

• $\sf S_n$ = Sum of n terms.
• a = First term of AP.
• d = Common difference of AP.