Question

There are 20 termss in an arithmetic
sequence sum of the first and last
terms is 88.
a) what is the sum of the 2nd and​

Answer 1

★ Correct Question : There are 20 terms in an arithmetic sequence sum of the first and last terms is 88.

a) What is the sum of the 2nd and 19th term ?

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★ Given :

$\bullet \:\sf number\: of \:terms\: (n) = 20\\\\\bullet \:\sf Sum\:of\:the\:first\:term\:and\:last\:term = 88$

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★ Solution :

⠀

$\underline{\dag\:\textbf{According to the Question :}}$

$:\implies\sf a + a_{n} = 88\\\\\\:\implies\sf a + a_{20} = 88\\\\\\:\implies\sf a + a + 19d = 88\;\;\;\;\;\;\sf {\Bigg\{ a_n = a + (n - 1) d \Bigg\}} \\\\\\:\implies\sf 2a + 19d = 88.....(1)\\\\\\:\implies\sf a_{2} + a_{19} = a + d + a + 18d\\\\\\:\implies\sf a_{2} + a_{19} = 2a + 19d\\\\\\:\implies\:{\underline{\boxed{\boxed{\bf a_{2} + a_{19} = 88}}}......\sf {\Bigg\{ using\: equation \:(1) \Bigg\} }}\:\bigstar$

$\therefore\:\underline{\textsf{Sum 2nd and 19th terms of sequence is \textbf{88}}}.$

Peace :) !

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