1. If -5a,b,16 are in A.P, Find the value of a and b.

2. An A.P has its terms and common differences of -3. Find Its first and Last term if its sum is (a)120 (b) 15

3. The first and last term of an A.P are 1 and
(a) The Number of terms in the A.P. Find
The common difference between them if the sum of it term is 544.

please send post the Answers Here! Thanks

1)5,a,b,16....
Common difference =a-5=16-b........ Eq 1
b-a=a-5.............eq2
From eq2, b+5=2a,
:. A=(b+5)/2..........eq3
Sub for a into eq1
((B+5)/2)-5=16-b
(B+5)/2=21-b
B+5=42-2b
3b=37
:.b=37/3=12 1/3

From eqq2, b+5)/2=a
37/3 + 5 )/2 =a
37+15)/3 x 1/2=a
52/3 x 1/2 =a
A=52/6= 8 4/6

brosss: 1)5,a,b,16....
Common difference =a-5=16-b........ Eq 1
b-a=a-5.............eq2
From eq2, b+5=2a,
:. A=(b+5)/2..........eq3
Sub for a into eq1
((B+5)/2)-5=16-b
(B+5)/2=21-b
B+5=42-2b
3b=37
:.b=37/3=12 1/3

From eqq2, b+5)/2=a
37/3 + 5 )/2 =a
37+15)/3 x 1/2=a
52/3 x 1/2 =a
A=52/6= 8 4/6

Tnx my Oga @ d Top!!! I appreciate plz solve others

Guy, did u modify the question, take time o.
Here's the new solution

-5a,b,16

16-d-d=-5a
16-2d=-5a............. Eq1 where d is common difference.
b-(-5a)=d
b+5a=d.............eq2
Also,
16-b=d.............eq3
By eliminating eq2 and 3,
(b-16)+(5a+b)=d-d
b-16+5a+b=0
-16=-5a
:.,a=3.2

Sub for a into eq1

16-2d=-5a
16-2d=-5(3.2)
16-2d=-16
d=32/2
d=16

From eq2,
b+5a=d
:. b+5(3.2)=16
b=16-16=0

U'ld have to retype the second and third question properly, you left out some variables.
Take your time and retype and I will provide the answer so you'ld get all three assignment questions.
Waiting.......

2. An A.P has its terms and common differences of -3. Find Its first and Last term if its sum is (a)120 (b) 15

3. The first and last term of an A.P are 1 and The Number of terms in the A.P. Find
The common difference between them if the sum of it term is 544.

It wasn't Modified

Ok, my bad, I probably read it wrong.....
if the quest is, 5,a,b,16 the 1st answer is correct
If the question is -5a,b,16 the second solution is correct.....

Let me explain what I meant by missing variables,
U provided the common difference in the second question as -3, but the nth term wasn't given, is it the 4th term of 50th term, something of such nature

The same applies to the last question....
The first and last term in an ap are 1 and --------
And the sum of its ---------- term is 544,

Hope you understand what I mean now..... Sorry about the modification thing

brosss: Ok, my bad, I probably read it wrong.....
if the quest is, 5,a,b,16 the 1st answer is correct
If the question is -5a,b,16 the second solution is correct.....

Let me explain what I meant by missing variables,
U provided the common difference in the second question as -3, but the nth term wasn't given, is it the 4th term of 50th term, something of such nature

The same applies to the last question....
The first and last term in an ap are 1 and --------
And the sum of its ---------- term is 544,

Hope you understand what I mean now..... Sorry about the modification thing

Plz give me ur Number!!!