Math, asked by Anonymous, 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 singhaashka915
2

Step-by-step explanation:

If the sum of the terms of the AP is 120, then find the number of terms and the common difference. Last term of an AP, l = 45. ... Therefore, the number of terms is 6 and the common difference is 10

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Answered by shantichandra036
1

Given, the first term of an AP, a = -5

Last term of an AP, l = 45.

Sum of the term of the AP, S = 120

We have to find the number of terms and the common difference.

We know that, if l is the last term of an AP, then the sum of the terms is given by

S = n/2[a+l]

So, 120 = n/2[-5+45]

120 = n/2[40]

120 = 20n

n = 120/20

n = 6

The nth term of an AP is given by

aₙ = a + (n - 1)d

Given, a₆ = 45

45 = -5 + (6 - 1)d

45 + 5 = 5d

50 = 5d

d = 50/5

d = 10

Therefore, the number of terms is 6 and the common difference is 10.

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