Question

The first and the 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 sum.

Answer 1

$\huge{\mathfrak{\red{\underline{Solution:-}}}}$

Given that :-

a = 7

l = 350

d = 9

let there be n terms in the A.P.

l = a + (n + 1)d

350 = 17 +(n - 1)

333 = ( n -1)9

(n - 1) = 37

n = 38

Sn = n/2 (a + l)

Sn = 38/2(17 + 350)

= 19(367)

= 6973 ( Answer )

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Answer 2

$\huge\bf\mathfrak{QUESTION\: :}$

The first and the 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 sum.

$\huge\bf\mathfrak{ANSWER \: :}$

$\large\bf\mathfrak{GIVEN\: :}$

In an AP consisting of n terms

first term=a=17

last term=l=an=350

common difference=d=9

$\large\bf\mathfrak{TO\:FIND\: :}$

no. of terms = n =?

Sum of all terms=Sn=?

$\large\bf\mathfrak{SOLUTION\: :}$

as we know that

an= a+(n-1)d

so here we have

a= 17, an=350, d=9, n=?

so an = a+(n-1)d

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

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

=> (n-1)= 333/9

=> n=37+1

=> n=38

=> no. of terms are 38

now we have to find Sn

but we know that

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

and also here we have

n=38 , a=17, l=an=350

so

=> Sn=(n/2) (a+l)

=> S(38)=(38/2) (17+350)

=> S(38)=19×367

=> S(38)=6973

=> sum of 38 terms are 6973

$\large\bf\mathfrak{HENCE\: :}$

no. of terms are 38 and there sum is 6973