Question :

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

Subject

Mathematics

Standard

Class 11

Views

2935

Asked By

Emily

Pari
Answer / Solution

Solution: Given that,
first term, a = 5
last term, l = 45
Sum of the AP, Sn = 400

As we know, the sum of AP formula is;
Sn = n/2 (a + l)
400 = n/2 (5 + 45)
400 = n/2 (50)
Number of terms, n = 16

As we know, the last term of AP series can be written as;
Last term, l = a + (n − 1) d
45 = 5 + (16 − 1) d
40 = 15d
Therefore,

Common difference, d = 40/15 = 8/3

Also Check : 2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboids.

Also Check : The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of the first sixteen terms of the AP.


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