Question

If five times the fifth term of an
a.P. Is equal to 8 times its eighth term, then what is the value of 13th term?

Answer 1

✨✨GIVEN÷

If five times the fifth term of an AP is equal to 8 times it's 8th term,.

i.e => 5(a5)=8(a8)

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✨✨ CONCEPT CLEARANCE.,✨✨

$5 \times (a + 4d) = 8 \times (a + 7d) \\ \\ 5a + 20d = 8a + 56d \\ \\ 5a - 8a = 56d - 20d \\ \\ - 3a = 36d \\ \\ a = \frac{ - 36}{3 } d \\ \\ \color{orange} \boxed{ a = - 12d} \\ \\ \\ a13 = a + 12d \\ \\ a13 = - 12d + 12d \\ \\ \color{green} \boxed{ a13 = 0}$

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✨Some other Important Formulas✨

$\color{red} \boxed{an = a + (n - 1)d}$

$\color{orange} \boxed{sn = \frac{n}{2} (2a + (n - 1)d \: )}$

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Answer 2

Answer:

$according -to- the -question,\\5*a5=8*a8\\5[a+4d]=8[a+7d]\\5a+20d=8a+56d\\5a-8a=56d-20d\\-3a=36d\\a=36d/-3\\a=-12d---Eqn1\\\\\\\\a13=a+12d--------Eqn2\\substiute Eqn 1 in Eqn 2\\a13=-12d+12d\\a13=0\\------------------\\------------------$

Step-by-step explanation:HOPE IT HELPS YOU