The first term of an A.P. is 5, the last term is 45 and the sum of all the terms is 400. Find the number of terms and th... | SA 3m | Maths | SuperPadhai

Arithmetic Progressions > Question

SA3 marksYear: 2024MediumCBSE Class 10

arithmetic-progressionssum-of-termscommon-difference

Question

The first term of an A.P. is 5, the last term is 45 and the sum of all the terms is 400. Find the number of terms and the common difference of the A.P.

Solution

1

a = 5

,

a_{n} = 45

,

S_{n} = 400

+0.5 marks

2

\frac{n}{2} (5 + 45) = 400 \Rightarrow 25 n = 400 \Rightarrow n = 16

+1 mark

3

5 + 15 d = 45 \Rightarrow 15 d = 40 \Rightarrow d = \frac{8}{3}

+1.5 marks

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