Question

A=7,a13=35,find d and s13 step by step

Answer 1

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a = 7
T13 = 35
n = 13

Tn = a+(n-1)d
35 = 7 + (13-1)×d
28 = 12×d
d = 28/12 = 7/3

Sn = n/2 [2a+(n-1)d]
= 13/2 [2×7 + (13-1)×7/3]
= 13/2 [14 + 28]
= 13/2 × 42
= 13 × 21
= 273

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Answer 2

Answer:

d = 7/3, Sn=273

Step-by-step explanation:

First term of an AP = a = 7

Thirteenth term of an AP = 35

a + 12d = 35 ------(1)

Substitute a in eq - (1)

a + 12d = 35

(7) + 12d = 35

12d = 35 - 7

12d = 28

d = 28/12

d = 7/3

In an AP sum of the terms = n/2 ( a + an )

= 13/2 ( 7 + 35)

= 13/2 ( 42)

= 13(21)

= 273