Question

First term of an As is 10 and sum of first five term is 250 wht is the sequence?​

Answer 1

Answer:

10,30,50......sequence ,,,

Answer 2

GIVEN :–

• First term of A.P. (a) = 10

• Sum of first five terms = 250

TO FIND :–

• A.P. = ?

SOLUTION :–

• If Common difference is 'd' then Sum of n terms is –

ㅤ

$\bf \large \implies{ \boxed{ \bf S_{n} = \dfrac{n}{2} \{2a + (n - 1)d \}}}$

ㅤ

• According to the question –

ㅤ

$\bf \implies S_{5} =250$

ㅤ

$\bf \implies \dfrac{5}{2} \{2(10) + (5 - 1)d \} =250$

ㅤ

$\bf \implies \dfrac{5}{2}(20 + 4d)=250$

ㅤ

$\bf \implies 20 + 4d=250 \times \dfrac{2}{5}$

ㅤ

$\bf \implies 20 + 4d=100$

ㅤ

$\bf \implies 4d=100 - 20$

ㅤ

$\bf \implies 4d=80$

ㅤ

$\bf \implies d= \cancel\dfrac{80}{4}$

ㅤ

$\bf \implies \large{ \boxed{ \bf d=20}}$

ㅤ

▪︎ Hence , A.P. –

ㅤ

$\bf \implies 10,30,50,70,..........$

ㅤ

$\rule{200}{4}$