Question

8.The 50th and 60th terms of an arithmetic progression are 100 and 120 respectively,then the 10 th term​

Answer 1

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The 50th and 60th terms of an A.P. are 100 & 120 respectively . Find the 10th term .

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★ Given :

• 50th term $(a_{50})=100$
• 60th term $(a_{60})=120$

★ To Find :

• 10th term $(a_{10})$=?

★ Solution :

• First term = a
• Common Difference = d
• no. of terms = n

We have the 50th & 60th term , so ,

using the Formula

$\boxed{ \rm \: n_{th} \: term \: \: or \: \: a _{n} = a + (n - 1)d}$

So ,

$\rm \mapsto \: a_{50} = a + (50 - 1)d$

$\mapsto \rm \: 100 = a + 49d$

$\mapsto \rm \: a = 100 - 49d.....(i)$

and

$\mapsto \rm \: a _{60} =a + (60 - 1)d$

$\mapsto \rm \: 120 = a + 59d$

now , put the value of a from eq(i)

$\mapsto \rm \: 120 = 100 - 49d + 59d$

$\mapsto \rm \: 120 - 100 = 10d$

$\mapsto \rm \cancel{10}d = \cancel{20}$

$\mapsto \boxed{ \rm \: d = 2}$

Put the value of d in eq (i)

$\mapsto \rm \: a = 100 - 49 \times 2$

$\mapsto \rm \: a = 100 - 98$

$\mapsto \boxed{\rm \: a = 2}$

Now , We have to Find the 10th term

So ,

Again using the Formula

$\mapsto \rm \: a _{10} = a + (10 - 1)d$

$\mapsto \rm \: a _{10} = 2 + 9 \times 2$

$\mapsto \rm \: a_{10} = 2 + 18$

$\large\mapsto \boxed{\rm \:a _{10} = 20}$

So ,

The 10th term of this Airihmetic Progression will be 20 .