Question

find fourth term of an AP whose first term is 5 and common difference is -5​

Answer 1

a=5

d= -5

n=4

a4= a+(n-1) d

=5+(4-1)-5

= 5-15

= -10.

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Answer 2

Given:

• First term of AP = 5
• Common difference = - 5

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To find:

• Fourth term of AP?

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Solution:

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$\star\;{\boxed{\sf{\pink{a_4 = a + 3d}}}}$

$\sf Here \begin{cases} & \sf{First\;term,\;a = \bf{5}} \\ & \sf{Common\; Difference,\;d = \bf{- 5}} \end{cases}$

$:\implies\sf a_4 = 5 + 3(-5)$

$:\implies\sf a_4 = 5 - 15$

$:\implies{\boxed{\sf{\purple{a_4 = - 10}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;fourth\;term\;of\;an;AP\:is\; \bf{-10}.}}}$

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$\boxed{\underline{\underline{\bigstar \: \bf\:Formula\:Related\:to\:AP\:\bigstar}}}$

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$\sf (i)\;The\; n^{th}\;term\;of\;an\;AP\; = \; \red{a_n + (n - 1)d}$

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$\sf (ii)\;Sum\;of\;n\;term\;of\;an\;AP\; = \; \purple{S_n = \dfrac{n}{2} \bigg\lgroup\sf 2a + (n - 1)d \bigg\rgroup}$

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$\sf (iii)\;Sum\;of\;all\;terms\;of\;AP\;having\;last\:term\;as\;'l'\; = \; \pink{ \dfrac{n}{2}(a + l)}$