Answer :
The sum of the first 10 terms of the AP is B 235.
How the sum of the first 10 terms of the AP is computed using the following formula:
Sₙ = n/2 (2a+(n−1)d)
Where:
Sₙ = Sum of the AP series
n = the number of terms
a = the value of the first term
d = the common difference
Common Difference of AP = 3
Common Ratio of a GP = 5
First term of the AP, a = 10
Fourth term of the AP, = 19
Therefore, the sum of the AP is given as:
= 10/2 (2 x 10 + (10 - 1)3)
= 5 (20 + (9)3)
= 5 (20 + 27)
= 235
Check:
Formula
[tex]a_{n}=a_{1}+(n-1)d[/tex]
[tex]a_n[/tex] = the nᵗʰ term in the sequence
[tex]a_1[/tex] = the first term in the sequence
[tex]d[/tex] = the common difference between terms
Alternatively, we can use the above check formula to find all the terms and sum manually.
Complete Question:
The common difference of an arithmetic progression is 3 and the common ratio of a geometric prepression is 5.Corresponding terms of the AP and GP is added form a new sequence. If the first and the fourth arms of this sequence are 10 and 19 respectively, then the sum of the first 10 terms of the AP is A 410 B 235 C 381 D 340
