Question

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

Answer 1

Answer:

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1. Total no. of terms = 6

2. Common Difference = 10

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Step-by-step explanation:

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See The Attachment My Friend....

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Answer 2

Given

The first term = -5

The last term = 45

Sum of n terms = 120

To Find

Number of terms = ?

Common Difference = ?

SOMETHING YOU NEED TO KNOW

Sₙ = n/2 (a+aₙ)

Sₙ = Sum of all terms

n = Number of terms

a = The first term

aₙ = The last term

$\implies 120=\dfrac{n}{2}(-5+45)$

$\implies 240 = 40n$

$\implies n = \dfrac{240}{40}$

$\implies n = 6$

$\boxed{\boxed{\bold{Therefore \ the \ total \ number \ of \ terms \ is \ 6}}}}}}}}$

Formula to be used

aₙ = a + (n-1)d

aₙ = The last term

a = The first term

n = Number of terms

d = Common Difference

$\implies 45=-5 + (n-1)d$

$\implies 45+5=6-1(d)$

$\implies 50=5d$

$\implies d = \dfrac{50}{5}$

$\implies d = 10$

$\boxed{\boxed{\bold{Therefore, \ the \ common \ difference \ is \ 10}}}}}}$