arithmetic progression?

Question

1.) find the number of terms in the given Arithmethic Progression
-3,-11,-19,-27,.....,-115

2.)Three terms are in Arithmetic progression. If their sum is 21 and the sum of their squares is 149, what are the numbers?

3.) find S(sub)15 in Arithmethic progression 1,-7, -15,...,-111

hope you could help me with these...
I need your answers to verify my answers..I ll also try solving these...pls include ur solution!

that would be greatly appreciated!

My answers

1.) I think its not 14 coz....I completed the series and theres 15 terms..

-3,-11,-19,-27,-35,-43,-51,-59,-67,-75,-83,-91,-99,-107,-115

Answer 1

1) -11 = -3 - 8
-19 = -11 -8 = -3 -8*2
-27 = -19 - 8 = -19 - 8*3
-115 = -3 - 8x
-8x = -112
x = -112 / -8 = 14 terms

2) x + (x+a) + (x+2a) = 21
x² + (x+a)² + (x+2a)² = 149
x = 6 and a = 1
Numbers : 6 ; 7 and 8

3) S1 = -7 = 1-8
S2 = -15 = -1 -8*2
S15 = -1 -8*15 = -119

Answer 2

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