Question

if seventh term of the ap is zero then what is the relationship between 17th term and 37th term​

Answer 1

Step-by-step explanation:

Given :-

seventh term of the AP is zero

To find :-

The relationship between 17th term and 37th term

Solution :-

Let the first term of an AP be a

Let the common difference be d

We know that

The general term of an AP = a+(n-1)d

Given that

Seventh term = 0

=> a+(7-1)d = 0

=> a+6d = 0

=> a = -6d

Therefore, a = -6d -------(1)

Now,

17th term = a+(17-1)d

=> 17th term = a+16d

=> 17th term = -6d+16d (from (1))

=> 17th term = (-6+16)d

=> 17th term = 10d

There 17th term = 10d -----(2)

and

37th term = a+(37-1)d

=> 37th term = a+36d

=> 37th term = -6d+36d (from (1))

=> 37th term = (-6+36)d

=> 37th term = 30d

Therefore, 37th term = 30d

=> 37th term = 3(10d) (from (2))

=> 37th term = 3×17th term

Therefore, 37th term = 3 ×17th term

Answer :-

The relationship between 17th term and 37th term of the AP is "37th term is 3 times to the 17th term" i.e.

37th term = 3 ×17th term.

Used formulae:-

→ The general term of an AP = a+(n-1)d

• a = First term
• d = Common difference
• n = Number of terms

Answer 2

Arithmetic Progression

We have given that the seventh term of AP is zero. And we have been asked to find the relationship between 17 th and 37 th term.

We know that, The General term of an AP = $\sf{a\:+\:(n\:-\:1)d}$

As the 7 th term is zero,

Let n = 7,

$\sf\implies{a\:+\:(7\:-\:1)d\:=\:0}$

$\sf\implies{a\:+\:(6)d\:=\:0}$

$\sf\implies{a\:=\:-6d}$ $\sf---(1)$

When n = 17,

$\sf\implies{a\:+\:(17\:-\:1)d}$

$\sf\implies{a\:+\:(16)d}$

Substituting 'a' (1) value, we get,

$\sf\implies{-6d\:+\:16d}$

$\sf\implies{-6\:+\:16d}$

$\sf\implies{10d}$ $\sf---(2)$

The 17 th term = 10d.

When n = 37,

$\sf\implies{a\:+\:(37\:-\:1)d}$

$\sf\implies{a\:+\:(36)d}$

Substituting 'a' value, we get,

$\sf\implies{-6d\:+\:36d}$

$\sf\implies{-6\:+\:36d}$

$\sf\implies{30d}$ $---(3)$

The 37 th term = 30d.

Comparing (2) & (3), we get,

We have found that 17 th term = 10d and 37 th term = 30d, And the relationship between them is 37 th term is 3 times 17 th term. That is, $\sf{30d\:=\:3\:\times\:10d}$, which is $\sf{30d\:=\:30d}$.

Hence, The relationship between 17 th term and 37 th term is 37 th term is 3 times 17 th term.