Question

The first term of an A.P is -76 and the sum of first 45 terms is -9360. Which of the following is the last term in this A.P ?​

Answer 1

Given :

• First term of an A.P = -76

• Sum of 45 terms = -9360

To find :

• last term of given A.P.

Formula used :

• Sn = n/2 ( a + l )

where :-

• sn = sum of n terms

• n = number of terms

• a = first term

• l = last term

Solution :

To find the last term of A.P use the given formula :-

⟹ Sn = n/2 ( a + l )

Now put :-

• Sn = -9360
• n = 45
• a = -76

⟹ -9360 = 45/2 ( -76+ l )

⟹ -9360 ×2 = 45 ( -76 + l )

⟹ - 18720 = 45 ( -76 + l )

⟹ - 18720 / 45 = -76 + l

⟹ -416 = -76 + l

⟹ -416 +76 = l

⟹ - 340 = l

Answer :

therefore last term = -340

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Verification of Answer :-

To verify your answer put l = -340 , a = -76 , n = 45 in Sn = n/2 ( a + l ). If you get -9360 as sum then your answer l = -340 is correct.

Sn = n/2 ( a + l ).

Sn = 45/2 ( -76-340 )

Sn = 45/2 ( - 416)

Sn = - 45× 208

Sn = -9360

Hence verified

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Learn more :-

1. Tn = a+(n-1)d

2. Sn = n/2[2a+(n-1)d]

3. Sn = n/2(a+l)

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