Question

if the 17th term of A.P excessed 10th term by 7th term the coomon difference​

Answer 1

Answer:

Let the 17th term be $A_{17} = a+(17-1)d$ and let the 10th term be $A_{10}= a+(10-1)d$ and the 7th term as $A_{7}=a+(7-1)d$

But the 17th term exceeds the 10th term by 7th term ⇒

$A_{17} = A_{10} + A_{7}$ ⇒

$a+(17-1)d=a+(10-1)d+a+(7-1)d$ ⇒

$a+16d= a+9d+a+6d$ ⇒

$a+16d=2a+15d$ ⇒

$a-2a=16d-16d$ ⇒

$-a=-d$⇒

$\frac{-a}{-1} =\frac{-d}{-1}$ ⇒

$a=d$ ∴

The common diffrence is $a =1st$ term of the AP

Step-by-step explanation: