Question

In a A.p, if a=5, a16=50 then find S16​

Answer 1

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Step-by-step explanation:

ANSWER ::

S16

= The sum of first 16 terms

= 16/2 ( 1st term + 16th term)

= 8× ( 5 + 50)

= 8× 55

= 440

Answer 2

Answer :-

Given :-

In a A.P ;

a = 5 , a16 = 50

Required to find :-

• Sum of the 16th terms ?

Formula used :-

$\large{\rightarrowtail{\boxed{\rm{{S}_{nth} = \dfrac{n}{2} [ 2a + ( n - 1 ) d ] }}}}$

Solution :-

Given that :-

a = 5

a16 = 50

we need to find the sum of 16 terms

So,

a = 5

a16 = 50

But 16th term can be written as

a16 = a + 15d

So,

a + 15d = 50

Consider this a equation 1 .

Now substitute the value of a in equation 1 .

So,

5 + 15d = 50

15d = 50 - 5

15d = 45

d = 45/15

d = 3

Hence,

d = 3

Using the formula ,

$\large{\rightarrowtail{\boxed{\rm{{S}_{nth} = \dfrac{n}{2} [ 2a + ( n - 1 ) d ] }}}}$

Here,

a = first term

d = common difference

n = the term number which you want to find

So,

$\longrightarrow{\tt{ {S}_{nth} = {S}_{16}}}$

$\rightarrowtail{\sf{ {S}_{16} = \dfrac{16}{2} [ 2 ( 5 ) + ( 16 - 1 ) 3] }}$

$\rightarrowtail{\sf{ {S}_{16} = \dfrac{16}{2} [ 2 ( 5 ) + 15 \times 3] }}$

$\rightarrowtail{\sf{ {S}_{16} = \dfrac{16}{2} [ 2 ( 5 ) + 45 ]}}$

$\rightarrowtail{\sf{ {S}_{16} = \dfrac{16}{2} [ 10 + 45 ]}}$

$\rightarrowtail{\sf{ {S}_{16} = \dfrac{16}{2} [ 55 ] }}$

$\rightarrowtail{\sf{ {S}_{16} = 8 \times 55 }}$

$\rightarrowtail{\sf{ {S}_{16} = 440 }}$

Therefore,

Sum of 16 terms is 440

Points to remember :-

1.

The first term of an arithmetic sequence is represented by " a "

2.

The common difference between the terms in the arithmetic progression is represented by " d "

3.

The simplified formula is ;

$\large{\rightarrowtail{\boxed{\rm{{S}_{nth} = \dfrac{n}{2} [First\;term\;+\;Last\;term] }}}}$