Question

16th term of an arithmetic sequence is 84 added to the 4th term. If the 24th term is 168 then
a) what is the common difference?
b) what is the first term?
c)find the sum of first 20 terms. ​

Answer 1

Answer:

SWER:

(i) The given progression 9, 15, 21, 27, ... .

Clearly, 15 − 9 = 21 − 15 = 27 − 21 = 6 (Constant)

Thus, each term differs from its preceding term by 6. So, the given progression is an AP.

First term = 9

Common difference = 6

Next term of the AP = 27 + 6 = 33

(ii) The given progression 11, 6, 1, −4, ... .

Clearly, 6 − 11 = 1 − 6 = −4 − 1 = −5 (Constant)

Thus, each term differs from its preceding term by −5. So, the given progression is an AP.

First term = 11

Common difference = −5

Next term of the AP = −4 + (−5) = −9

(iii) The given progression −1, -56, -23, -12, ...

Clearly, -56-(-1)=-23-(-56)=-12-(-23)=16 (Constant)

Thus, each term differs from its preceding term by 16. So, the given progression is an AP.

First term = −1

Common difference = 16

Next term of the AP = -12+16=-26=-13

(iv) The given progression √2, √8, √18, √32, ...

This sequence can be re-written as √2, 2√2, 3√2, 4√2, ...

Clearly, 2√2-√2=3√2-2√2=4√2-3√2=√2 (Constant)

Thus, each term differs from its preceding term by √2. So, the given progression is an AP.

First term = √2

Common difference = √2

Next term of the AP = 4√2+√2=5√2=√50

(v) The given progression √20, √45, √80, √125, ...

This sequence can be re-written as 2√5, 3√5, 4√5, 5√5, ...

Clearly, 3√5-2√5=4√5-3√5=5√5-4√5=√5 (Constant)

Thus, each term differs from its preceding term by √5. So, the given progression is an AP.

First term = 2√5=√20

Common difference = √5

Next term of the AP = 5√5+√5=6√5=√180

Step-by-step explanation:

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