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Step-by-step explanation:
Given, first term, a = 10
Last term, a
l
= 361
And, common difference, d = 9
Now a
l
=a + (n −1)d
⟹ 361 = 10 + (n − 1)9
⟹ 361 = 10 + 9n − 9
⟹ 361 = 9n + 1
⟹ 9n = 360
⟹ n = 40
Therefore, total number of terms in AP = 40
Now, sum of total number of terms of an AP is given as:
S
n
= n/2 [2a + (n − 1)d]
⟹ S
40
= 40/2 [2 × 10 + (40 − 1)9]
= 20[20 + 39 x 9]
=20[20 + 351]
=20 × 371 = 7420
Thus, sum of all 40 terms of AP = 7420
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