Question

Find the sum of first term of an A.P of which
the 6th term is 45 ?​

Answer 1

Answer:

The sum of first 11 term of an A.P of which the 6th term is 45 is 495.

Answer 2

Answer:

Formula of nth term of AP = a_n=a+(n-1)da

n

=a+(n−1)d

where a is the first term

d is the common difference

n = No. of terms

a_na

n

= nth term

Substitute n = 6

a_6=a+(6-1)da

6

=a+(6−1)d

a_6=a+5da

6

=a+5d

6th term is 45

So, a+5d=45 --- 1

Formula of sum of first n terms =S_n=\frac{n}{2}(2a+(n-1)d)S

n

=

2

n

(2a+(n−1)d)

Substitute n = 11

S_{11}=\frac{11}{2}(2a+(11-1)d)S

11

=

2

11

(2a+(11−1)d)

S_{11}=\frac{11}{2}(2a+10d)S

11

=

2

11

(2a+10d)

S_{11}=\frac{11}{2}(2)(a+5d)S

11

=

2

11

(2)(a+5d)

Using 1

S_{11}=\frac{11}{2}(2)(45)S

11

=

2

11

(2)(45)

S_{11}=495S

11

=495

Hence the sum of first 11 term of an A.P of which the 6th term is 45 is 495

Find the sum of 32 terms of an A.P . whose 3rd term is 1 and 6th term is -11

Step-by-step explanation:

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