Question

the 25th term of a series is 44.5 the sum of the first 30 terms is 76.5 find the 16th term

Answer 1

Answer:

Step-by-step explanation:

let us take the given series is in A.P (not given)

25th term  =  a + 24d = 44.5  -------- (1)

also, $\frac{30}{2}$[2a+29d] = 76.5

=>  15* [2a+29d] = 76.5

=>   2a+29d = 76.5/15

=>  2a+29d = 5.1  -------------- (2)

(1)*2 - (2)=>  2a+48d = 89.0

             -     2a+29d =   5.1  

                          19d = 83.9

if G.P,

ar²³ = 44.5

a(r³⁰-1) / 30-1  = 76.5

ar³⁰ - a = 76.5*29

ar³⁰ - a = 2218.5

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