if the sum of first 14 terms of an AP is 1050 and its first term is 10, find the 20th term.

if the sum of first 14 terms of an AP is 1050 and its first term is 10

1.	if the sum of first 14 terms of an AP is 1050 and its first term is 10, find the 20th term.
Answer» Given, a = 10, and S14\xa0= 1050Let the common difference of the A.P. be d{tex}\\therefore \\quad S _ { n } = \\frac { n } { 2 } [ 2 a + ( n - 1 ) d ]{/tex}{tex}\\therefore \\quad S _ { 14 } = \\frac { 14 } { 2 } [ 2 \\times 10 + ( 14 - 1 ) d ]{/tex}\xa01050 = {tex}7 (20 + 13 d ){/tex}{tex}20 + 13d{/tex} =\xa0{tex}\\frac{1050}{7}{/tex}\xa0{tex}20 + 13d{/tex} = 150{tex}13d{/tex} = 150 - 20{tex}13d{/tex} = 130{tex}d{/tex} =\xa0{tex}\\frac{130}{13}{/tex}\xa0= 10{tex}a_{20} = a + (n - 1)d{/tex}= 10 + (20 - 1) 10= 10 + 19\xa0{tex}\\times{/tex}\xa010= 10 + 190= 200Hence, a20\xa0= 200