Question

Find the 20th term from the last term of the A.P. 3, 8, 13, …, 253.​

Answer 1

AnswEr:

Given

AP is 3,8,13.... 253

To Find :-

20th Term from the last Term of AP

Explanation:-

We can Write the Given AP in reverse Order

253,248,243......... 13,8,3

First Term (a) = 253

Common Difference = $\sf\: a_2 \:-\:a_1$

$:\implies\sf\: 248 \:-\: 253$

$:\implies\large\boxed{\sf{\red{d\:=\:-5}}}$

$\bold{\underline{\sf{By \: Using\; Formula}}}$

$\bigstar\large{\underline{\boxed{\sf{\pink{an \:=\; a\;+\;(n\:-\;1)d}}}}}$

Putting Values

$:\implies\sf\: 253 + 19 (-5)$

$:\implies\sf\: 253 - 95$

$:\implies\large\boxed{\sf{\red{158}}}$

$\small\bold{\underline{\sf{Hence,\;20th\:term\;from\;the\;last\;of\;AP\;is\:158.}}}$

Answer 2

$\mathtt{ \huge{ \fbox{Solution :)}}}$

Given ,

The AP is 3 , 8 , 13 , … , 253

Let us assume that , the sequence is 253 , 248 , 243 , ... , 3

Here ,

• First term (a) = 253
• Common difference (d) = -5

We know that , the general formula of an AP is given by

$\large \mathtt{\fbox{ a_{n} = a + (n - 1)d }}$

Substitute the known values , we get

$\sf \mapsto a_{20} = 253 + (20 - 1)( - 5) \\ \\\sf \mapsto a_{20} = 253 + (19)( - 5)\\ \\ \sf \mapsto a_{20} =253 - 95 \\ \\\sf \mapsto a_{20} = 158$

Hence , the 20th term of an AP from the last term is 158

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