#### Question

The first and the last terms of an A.P. are 34 and 700 respectively. If the common difference is 18, how many terms are there and what is their sum?

#### Solution

Let there be n terms in this A.P

First-term a = 34

Common difference d = 18

Last term l = 700

`=>a + (n - 1)d = 700`

`=> 34 + (n - 1) xx 18 = 700`

`=> (n - 1)xx 18 = 666`

=> n - 1 = 37

=> n = 38

Sum of first n terms = `n/2 [a + l] = 38/2 [34 + 700] = 19 xx 734 = 13946`

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Solution The First and the Last Terms of an A.P. Are 34 and 700 Respectively. If the Common Difference is 18, How Many Terms Are There and What is Their Sum? Concept: Arithmetic Progression - Finding Sum of Their First ‘N’ Terms..