Question

the number of terms in an ap is even the sum of odd terms is 24 and the sum of even terms is 30 the last term exceeds first term by 10.5 .then the number of terms in ap​

Answer 1

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Answer 2

Answer:

Total number of terms are 8.

Step-by-step explanation:

Let a, d and 2n be the first term, common difference and total of terms of an A.P. respectively, ie.,

$a+(a+d)+(a+2d)+..+(a+(2n-1)d)$

Number of even terms = n

Number of odd terms = n

Sum of odd terms :

$S_o\;=\;\frac{n}{2}[2a+(n-1)(2d)\;=\;24$

Sum of even terms :

$S_e\;=\;\frac{n}{2}[2(a+d)+(n-1)2d]\;=\;30$

Subtracting the equations, we get:

Also given,

$a+(2n-1)d\;=\;a+\frac{21}{2}$

$d\;=\;\frac{3}{2}$ , $n\;=\;\frac{6\times2}{3}$ $\;=\;4$

Total number of terms:

∴ $2n\;=\;2\times4\;=\;8$