Question

please answer this question ​

Answer 1

${\underbrace{\mathfrak{\gray{ <u>Given</u> :}}}}$

First term of an A. P.(Arithmetic progression) (a): 17

And the last term is( $\bf{{a}_{n}}$) : 350.

And also,

The common difference (d) = 9

${\underbrace{\mathfrak{\gray{ To \: find :}}}}$

How may terms are there and what is thier sum.

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${\underbrace{\mathfrak{\gray{ <u>Solu</u><u>tion</u> :}}}}$

We know that,

${ \underline{ \boxed{\sf{{a}_{n}} = a + ( n - 1) d }}}$

Where,

→ a (first term) = 17.

→ $\bf{{a}_{n}}$(Last term) = 350.

→ d (common difference) = 9.

Procedure :

By substituting the given values :

$\sf \leadsto \: 350 = 17 + (n - 1)9$

$\sf \leadsto \: 350 - 17 = (n - 1)9$

$\sf \leadsto \: 333 = ( n- 1)9$

$\sf \leadsto \: { \cancel{\frac{333}{9}}} = ( n- 1)$

$\sf \leadsto \: n- 1 = 37$

$\sf \leadsto \: n = 37 + 1$

$\bf \therefore \: n = 38$

After solving we get :

→ n = 38.

Again,

To find the no. of terms between them and their sum

Using the formula :

${ \underline{ \boxed{ \sf {S}_{n} = \frac{n}{2} \{a + a_n \}}}}$

Where,

n(no. of terms) = 38.

a(first term) = 17.

$\bf{{a}_{n}}$(Last term) = 350.

Substituting the values as follows :

$\sf \longmapsto {S}_{38} = \frac{38}{2} \{17 + 350 \}$

$\sf \longmapsto {S}_{38} = 19 \{367 \}$

$\sf \therefore {S}_{38} =6973 \: ans.$

${\underbrace{\mathfrak{\gray{Required \:\: answer :}}}}$

No. of terms (a) = 38 ans.

Sum of the terms $\sf {S}_{n}$= 6973 ans.

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