Question

sum of 1st 15 terms of an arithmetic sequence is 900 and 1st term is 4. find the 8th term. what is common difference. write the sequence​​

Answer 1

Answer:

Step-by-step explanation:

Given,

Sum of first 15 terms in a sequence(S_15) = 900

First term(a) = 4

To Find :-

1) 8th term(a_8)

2) common difference(d)

3) sequence

Formula Required :-

Sum of n terms of A.P :-

$s_n=\dfrac{n}{2}[2a+(n-1)d]$

nth term of an A.P :-

$a_n=a+(n-1)d$

Sequence of an A.P :-

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

Solution :-

Sum of first 15 terms in a sequence(S_15) = 900

$\implies 900=\dfrac{15}{2}[2(4)+(15-1)d]$

$900\times 2 = 15[8+14d]$

1800 = 15[8 + 14d]

1800/15 = 8 + 14d

120 = 8 + 14d

120 - 8 = 14d

112 = 14d

112/14 = d

∴ common difference(d) = 8

8th term of A.P :-

$a_8=a+(8-1)d$

$=4+7(8)$

= 4 + 56

= 60

$\therefore a_8=60$

Sequence of A.P :-

4 , 4 + 8 , 4 + 2(8) , 4 + 3(8) ..

= 4 , 12 , 20 , 28 ..

∴ Sequence of A.P= 4 , 12 , 20 , 28 ..