Question

Find the ratio of the sum of the first 24 and 36 terms of the A.P. 5, 8, 11, 14, …

Answer 1

Answer:

• 37:55

Explanation:

Given A. P. :—

• 5, 8, 11, 14,

nth term of an A.P. is given by,

$\implies \rm a_n = a + (n - 1)d$

Where,

• a is the first term
• n denotes the number of terms
• d is the common difference.

We have,

• a = 5
• d = 3

∴ Calculating $\bf a_{24}$ :-

$\implies \rm a_{24} = 5 + (24 - 1)3$

$\implies \rm a_{24} = 5 + (23)3$

$\implies \rm a_{24} = 5 + 69$

$\implies \rm a_{24} = 74$

Also, calculating $\bf a_{36}$ :-

$\implies \rm a_{36} = 5 + (36 - 1)3$

$\implies \rm a_{36} = 5 + (35)3$

$\implies \rm a_{36} = 5 + 105$

$\implies \rm a_{36} = 110$

$\rm \therefore \: Ratio = a_{24} : a_{36}$

$= 74 : 110$

$= 37 : 55$

Required answer:- 37 : 55

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