Question

4. The 11th term of the AP: - 5, - 5/2, 0, 5/2 , ..is (A) -20 (B) 20 (C)-30 (D) 30

Answer 1

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MATHS

The first term of an A.P. is 6 and the common difference is 5. Find the A.P. and its general term.

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ANSWER

It is given that the first term of an A.P is a=6 and the common difference is d=5.

Let us find the following terms:

a+d=6+5=11

a+2d=6+(2×5)=6+10=16

a+3d=6+(3×5)=6+15=21

We know that the general form of an arithmetic progression with first term a and common difference d is a,a+d,a+2d,......

General term=a

n

=a+(n−1)d

Hence, the required A.P is 6,11,16,21,.....

Answer 2

GiveN :-

• First term = - 5

• Common difference = - 5/2 - ( - 5 ) = 5/2

• Number of terms = 11

To FinD :-

• 11th term of the given A.P

SolutioN :-

By using A.P formula :

$\large:\implies \boxed{\bf \blue{ A_n = a + ( n-1)d}} \\ \\:\implies \sf A_{11} = - 5 + (11 - 1) \times \frac{5}{2} \\ \\:\implies \sf A_{11} = - 5 + 10 \times \frac{5}{2} \\ \\:\implies \sf A_{11} = - 5 + 5 \times 5 \\ \\:\implies \sf A_{11} = - 5 + 25 \\ \\ :\implies \boxed{ \sf A_{11} = 20}$

$\large \therefore \underline {\bf \green{11th \: term \: of \: AP \: is \: 20}}$