Question

#Quality Question
@Sequence And Series


Find an arthematic progression whose
first term is 20 and Sum of 1st 5 terms is 250 .

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Answer 1

▪Given :-

For an Arthematic Progression

First term = a = 20

and

Sum of 1st 5 terms = $\sf S_{5}$ = 250

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▪To Find :-

The A.P. OR Arthematic Progression

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▪Main Formula :-

For an A.P Sum of first n terms is given by :

$\bf S _{n} = \dfrac{n}{2} \bigg \{ 2a + (n - 1)d\bigg \}$

Where ,

• a = First term
• d = Common difference
• n = number of terms

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▪Solution :-

Here ,

a = 20

and

$\sf S_{5}$ = 250

So, n = 5

Let Common difference = d

Using Formula For Sum :

$250 = \dfrac{5}{2} \bigg \{2 \times 10 + (5 - 1)d \bigg \} \\ \\ 500 = 5(20 + 4d) \\ \\ 500 = 100 + 20d \\ \\ \sf20d = 400 \\ \\ \purple{ \Large\implies  \underline {\boxed{{\bf d = 20} }}}$

We Know that,

An A.P having first term a and common difference d is :

a , a + d , a + 2d , a + 3d , . . .

So ,

Required A.P. is :

$\huge \mathfrak{10 , 30 , 50 , 70 , \: .\: . \: .}$

$\Large \red{\mathfrak{  \text{W}hich \:   \: is  \:  \: the  \:  \: required} }\\ \huge \red{\mathfrak{ \text{ A}nswer.}}$

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Answer 2

Answer:

10, 30, 50...

Step-by-step explanation:

Given, a = 10.

Let the common difference be d.

Sum of n terms: (n/2) [2a + (n - 1)d]

Sum of 5 terms = (5/2) [2(10) + (5 - 1)d]

=> 250 = (5/2) [20 + 4d]

=> 100 = 20 + 4d

=> 80 = 4d

=> 20 = d

Therefore, the sequence is:

a = 10

a + d = 10 + 20 = 30

a + 2d = 10 + 40 = 50