If the 8th term of an ap is 31

Asked by admin @ 20/08/2021 in Math viewed by 312 People

If 8th term of an ap is 31 and 15th term is 16 more than 11th term find ap

Answered by admin @ 20/08/2021

Answer:

Required A.P: 3,7,11,15,...

Step-by-step explanation:

Let a and d are first term and common difference of an A.P.

$We \:know \: that,\\n^{th}\:term (a_{n}) = a+(n-1)d$

$Given \: 8^{th}\: term =31\\$

$\implies a+(8-1)d=31\\\implies a+7d=31\:---(1)$

According to the problem given, we get

$a_{15}-a_{11}=16$

$\implies a+14d-(a+10d)=16$

$\implies a+14d-a-10d=16$

$\implies 4d=16$

$\implies d =\frac{16}{4}=4$

/* Substitute d = 4 in equation (1), we get

$a+7\times 4 = 31$

$\implies a+28=31$

$\implies a = 31-28=3$

Now, Required A.P:

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

3,3+4,3+8,3+12,...,

3,7,11,15,...

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