Math, asked by virajudaysingh, 10 days ago

The first term of an ap is -5 and the last term is 45. If the sum of the terms of ap is 120 then find the number of terms and the common difference

Answers

Answered by jaditi2468gmailcom
1

Answer:

Let us consider an A.P. whose first term and common difference are a and d respectively.

Here, a=−5,a

n

=45,S

n

=120

Now, S

n

=

2

n

[2a+(n−1)d]=

2

n

[a+a+(n−1)d]

⇒S

n

=

2

n

[a+a

n

][a

n

=last term]

⇒120=

2

n

[−5+45]

⇒120=

2

n

×40

⇒n=

40

120×2

=6

⇒n=6

Hence, the number of terms =6

Now, a

n

=a+(n−1)d

⇒45=−5+(6−1)d

⇒45+5=5d

⇒5d=50

⇒d=10

Hence, the number of terms and the common difference of the A.P. are 6 and 10 respectively

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