5) if the 10th term of an Ap is 52 and 17th term is 20 more than the 13th term, find the 13th term
Arithmetic expressions
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5) if the 10th term of an Ap is 52 and 17th term is 20 more than the 13th term, find the 13th term
Arithmetic expressions
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Answer:
a+9d=52
a+16d=20+a+12d
4d=20
a=5
substitute in eq 1
a+9(5)=52
a=7
Verified answer
[tex]\huge\underline\mathbb{\red S\pink{O}\purple{L} \blue{UT} \orange{I}\green{ON :}}[/tex]
★ Given that,
↪ 10th term of AP is 52.
[tex]\tt\:⟹ a_{10}\:—\:a + 9d = 52....(i)[/tex]
↪ 17th term is 20 more than the 13th term.
[tex]\tt\:⟹a + 16d = (a + 12d) + 20[/tex]
[tex]\tt\:⟹ 5d = 20[/tex]
[tex]\tt\:⟹d = \frac{20}{5} [/tex]
[tex]\tt\:⟹d = 5[/tex]
[tex] \boxed{∴d = 5}[/tex]
[tex]\tt\:⟹a + 9(5) = 52[/tex]
[tex]\tt\:⟹ a + 45 = 52[/tex]
[tex]\tt\:⟹ a = 52- 45[/tex]
[tex]\tt\:⟹a = 7[/tex]
[tex]\boxed{∴a = 7}[/tex]
[tex]\tt\:⟹a_{13}=a + 12d[/tex]
[tex]\tt\:⟹ a_{13} = 7 + 12(5)[/tex]
[tex]\tt\:⟹ a_{13}=7 + 60[/tex]
[tex]\tt\:⟹ a_{13}= 67[/tex]
[tex]\underline{\boxed{\bf{\purple{∴ The \: value \: of \: a_{13} \: = \: 67}}}}[/tex]