Question

The first and last term of an AP are 17 and 350 respectively .if the common difference is 9 how many terms are there and what is their term.

Answer 1

Answer:

If the common difference is 9, how many terms are there and what is their sum ? Hence, there are 28 terms.

Answer 2

Answer:

Let a and d be the first term and common difference for an AP.

number of terms of AP = n

last term = nth term = l

Given:

a = 17

d = 9 ,

l = 350

a + ( n - 1 ) d=nth term

=> 35017 + ( n - 1 ) 9 = 350

=>( n - 1 ) 9 = 350 - 17

=>( n - 1 ) 9 = 333

=>n - 1 = 333 /9

=>n - 1 = 37

=>n = 37 + 1

=>n = 38

Therefore ,

Number of terms in given AP =

$\pink{\bold{n=38}}$

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The terms are:-

$\red{17, 26, 35....350}$

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Additional:

How to find the sum of the terms of AP?

let Sum of n terms of AP = Sn

We know,

Sn = n /2 ( a + l )

Here n= 38 (as we calculated)

putting values we get:

Sum = 38 / 2 [ 17 + 350 ]

= 19 × 367

= 6973