Question

How many term of arithmetic sequence 5,11,17,... must be added to get 385 ?​

Answer 1

Given sequence is 5, 11, 17 .....

The sum of the terms in the series upto a particular term equals 385.

Let that particular term be x.

So,

5+11+17+.......+x = 385

x = a + (n-1)d

where a is 1st term

n is nth term term in the series

d is common difference.

x = 5+(n-1)6

x = 5 + 6n - 6

x = 6n - 1

sum of the terms of an A.P upto nth term = n/2(2a + (n-1)d)

So,

5+11+17+.....x = n/2(10 + 6n - 6)

385 = n/2(6n + 4)

3n² + 2n - 385 = 0

3n² + 35n - 33n - 385 = 0

n(3n + 35) - 11(3n + 35) = 0

(3n + 35)(n - 11) = 0

n is a natural number.

So, n = 11

11 terms of the given series should be added to get a sum of 385.

Answer 2

The number of terms  which must be added in arithmetic sequence 5,11,17,to get 385 is 8.

Step-by-step explanation:

Given:

The Arithmetic sequence is  5,11,17,...

To get sum of arithmetic sequence 385.

To Find:

The number of terms  which must be added in arithmetic sequence 5,11,17,to get 385.

Formula Used:

$Z_{n} =\frac{n}{2} [2u+(n-1) v]$                    ---------------- formula no.01

Where,

Zn=  the sum of  n  terms of  A.P.

u=  the first term of A.P.

v=  the difference between the terms of A.P.

n = the number of terms of A.P.

Solution:

As given- arithmetic sequence 5,11,17,...

First term u =5   and common difference $v=11-5=6$

As given-to get sum of arithmetic sequence 385.

Sum of arithmetic sequence Zn =385

Putting value of u, v and Zn in formula no.1.

$Z_{n} =\frac{n}{2} [2u+(n-1) v]$

$385=\frac{n}{2} [2\times 5+(n-1)\times6]$

$385=\frac{n}{2} [10+ 6n-6 ]$

$385=\frac{n}{2} [4+ 6n]$

$385=\frac{n}{2} [2(2+ 3n)]$

$385=n(2+ 3n)$

$3n^{2} +2n-385=0$

$3n^{2} +35n-33n-385=0\\n(3n+35)-11(3n+35)=0\\(n-11) (3n+35)=0\\( n-11) =0\\n=11\\(3n+35)=0\\n=-\frac{35}{3} ( n\ can\ not\ be\ negative)$

Hence , the value of n is 11.

The no of terms must be added arithmetic sequence $=11-3=8\ terms.$

Thus, the number of terms  which must be added in arithmetic sequence 5,11,17,to get 385 is 8.

PROJECT CODE #SPJ3